(Note: If you are only interested in pictures, skip past this and hit “Continue Reading”)
This is a historical phenomenon, which entertains and fascinates me to no end. Buddhism had a huge impact on all East Asian cultures, especially on their pantheons of deities. On first glance it might seem odd that a reform movement, which rejected many of the core tenants of Vedic religion would transmit a belief in Vedic deities. This apparent oddity is a misunderstanding of Buddhism’s “atheism,” and a misunderstanding of what a “Deva” actually is. Most forms of Buddhism, while rejecting the concept of all-powerful gods or creator deities, openly accept the existence of powerful supernatural beings. This includes yakshas (nature spirits) rakshasas (demons) gandharvas (celestial musicians) nagas (supernatural snakes) and many other beings, including Devas (deities.) In Hindu and Buddhist cosmology, Devas are created beings that roam around the universe seeking the divine, albeit very powerful ones with much greater spiritual capabilities than humans. Hindu traditions tend to accord Devas much more power and divinity than Buddhism, and worship them as manifestations of The Supreme. In the Buddhist pantheon, the Devas have generally converted to Buddhism and now serve as his protectors, the protectors of his teachings, or as helpers to mortals who are trying to achieve enlightenment.
The reader should be aware that in Japanese mythology and theology the below deities freely interact with native Shinto deities, and deities imported from China. I am isolating the Indian derived deities for the purpose of this bog post, but do not be deluded into thinking that they are unintegrated with the rest of Japanese mythology.
The more popular of these deities are used in non-esoteric Mahayana Buddhism (the bulk of Buddhist sects in Japan.) However, most of these are relatively obscure deities because they are only used in the Shingon school, an esoteric (tantric) school of Buddhism. As such, the bulk of these Devas achieved full development in Japan around the late 700s or early 800s, as a result of the rise in popularity (especially amongst the political elite) of esoteric and Shingon Buddhism.
Last note: There are a lot of different names involved here, because (among other reasons) Sanskrit and Japanese don’t transliterate very well. For deities in which two names are listed, the first is Sanskrit, and the second is Japanese. In cases where, for some reason, I’ve listed many names, I will specify with an (S) or a (J) which language it is from.
(S) Ganesha/ (S) Vinayaka / (J) Binayaka / (J) Shoten/ (J) Kangiten: Ganesha was one of the first Indian deities to transit to Japan, and as in India, is one of the most popular in both esoteric and non-esoteric sects. Perhaps this is because his association with worldly prosperity has been retained, or perhaps amplified into a general association with pleasure. Thus, actors, geishas, gamblers, restaurant proprietors, etc offer him worship. Shoten has retained the association for removing obstacles, although his ancient association with creating obstacles which has long since been expunged from the Hindu tradition is still mildly active in Japan for reasons which will become clear later.
He is often depicted in (implicitly erotic) embrace with another elephant headed figure. In that iconography, his name is “Kangiten” or “Binayaka.” This is an allusion to a Japanese myth about Kangiten’s “evil” origins, wherein his mother, Uma births 1,500 evil children onto her left (collectively called Binayakas), the first of which was Binayaka. On her right side she births 1,500 good children the first of which was Avalokiteśvara/Kannon (the Bodhisatva of compassion) incarnated as Idaten (Skanda or Murugan in India.) In order to win Binayaka over to goodness, Idaten reincarnates as a female binayaka and becomes Kangiten’s wife. The bliss generated by their union turns Kangiten good. According to this myth therefore, the embracing Kangiten figures actually represent Kangiten in sexual union with his brother reincarnated as his wife/sister. There are other myths, which seek to explain this iconography, but all of them involve some sort of gender reversal, usually by means of reincarnation. There is a huge corpus of Japanese Ganesha myths, which do not exist at all in India, but the initial one just mentioned seems to almost reference Ganesha’s actual historical development in India. Ganesha probably evolved from the set of demons called Vinayakas/Binayakas who were known for erecting obstacles and creating divisions between allies. However, they were easily appeased. So easily appeased in fact that over time they evolved into positive forces, and merged into one deity—Ganesha.
However, the aforementioned Japanese myths all seem to be trying to explain the dual figured Kangiten iconography by posing, as it’s mythological basis. The real basis lies elsewhere, probably in the translations of Amoghavajra, a half Indian half Sogdian monk living in China in the early 700s. He was a founder of the “Chen-Yen” school of esoteric Buddhism (a precursor to the Shingon school,) and his translations of various tantric texts entail repeated references to the “dual-bodied Vinayaka” which is an obstacle removing and prosperity inducing deity described as looking exactly like modern embracing Kangiten figures, including the erotic embrace. There was also a pre-Buddhist Japanese deity named N-io, which took the form of a male and female in embrace, which could have contributed, or facilitated the popularity of the embracing Kangiten figures.
(S) Shiva/ (S) Mahakala/ (J) Daikoku-ten: Daikoku-ten is the most popular manifestation of Shiva (also known as Mahakala), although he is also the most different from the Indian version. His traditional trishula style trident has been replaced by a magic, prosperity-producing mallet. He is one of the Seven Lucky Gods, and as such carries a sack of treasure on his shoulder symbolizing wealth, wisdom, and patience. An association with wealth has wholly supplanted his association with destruction. Daikoku-ten’s jovial appearance is a far cry from Rudra, The Howler who struck terror into the hearts of Vedic era Indians. However, According to the Chinese pilgrim I-Tsing, this shift to a softer less frightening protective deity was already well underway in Western India by the 7th century (around the time when Buddhism began gaining large numbers of Japanese adherents). Daikoku-ten images are also commonly found in kitchens, a tradition possibly imported from China or India where Mahakala images were put in monastery kitchens. 
However, Daikoku-ten can also be manifested in 6 different forms, one of them being his consort, Kali, and another one is his son. For more details click here.
Shiva/Daijizaiten: This is the form of Shiva, which more resembles the Indian version. Daijizaiten is a protective deity, and takes on Shiva’s classical role as defender of the northeast. Some depictions retain the dark skin, while others do not but a fierce aspect is usually present. In Medieval times, Japan was considered the home of Shiva, and he was thought to be its cosmic ruler. He was also thought to be the creator of the Chinese writing system. 
Shiva can also be manifested as a part of Sanmen Daikoku, an amalgam deity consisting of Shiva (now in Daikoku form once again), Kubera, and Saraswati.
Shiva, Kubera, and Saraswati/Sanmen Daikoku: This is a three-headed deity which was invented relatively late– the late 14th century. A fierce aspect is sometimes depicted, but it doesn’t seem integral to the deity. See the following two entries for information on the Japanese forms of Kubera and Saraswati. 
Saraswati/Benzaiten: Another one of the Seven Lucky Gods. Her stringed instrument has switched nationalities, from an Indian veena to a Japanese biwa. She has retained her association with waters, music, language and knowledge. The emphasis on physical beauty seems to have heightened in the Japanese version. Overall she seems to have been transmitted to Japan without much major change. She has become the bodhisattva of entertainers, similar to how musicians worship Saraswati in India. Shinto worshippers have also adopted her as a kami. 
Kubera/Bishamon: In Japan Kubera does double duty as another one of the Seven Lucky Gods, and also as the Heavenly King of the North. Heavenly Kings are guardians of the cardinal directions, and Kubera is the only Hindu Deva to become one, the rest being novel Buddhist creations. In stark contrast to Kubera’s relatively mild portrayal in India and other parts of the Buddhist world, Bishamon is an enforcer of justice and a god of war. His prominence in Japan far outstrips his prominence in India. Statues of him are often used as a temple guardians, and his depictions are accordingly fearsome. It almost seems like Kubera and Shiva’s Daikoku-ten form switched roles when exported to Japan. Bishamon even holds a trident, reminiscent of Shiva.  
(S) Indra/ (S) Shakra / (J) Taishakuten: He not changed much from the Indian Buddhist version (which has already expunged the Hindu association with warfare.) Like Indra and Shakra, Taishakuten is the lord of storms, commands the Four Heavenly Kings, and lives atop Mt. Meru. He has even retained his elephant mount, which I imagine must have been difficult for Japanese sculptors who had never seen a photograph of an elephant. As the king of weather, he is also the commander of the Four Heavenly Kings. He also contributed to the evolution of the thunder god Raijin which will be addressed later. Japanese folk tales have cited Taishakuten and his wife (Shachi) as an example of the ideal romantic couple, much like Ram and Sita are in India. 
Yama/Enma: Yama doesn’t seem to have undergone major changes from the standard Buddhist version to his Japanese incarnation. He is still the “God of Death,” king of the underworld, and judge of the dead, and consequently has a fearsome aspect to represent death and justice. The only major difference is that he sometimes manifests as 10 different judges, one for each layer of the underworld. His Indian style crown is gone, replaced by a Japanese judge’s cap (sometimes with the word for “King” on it) and gown.
Garuda/Karura: I hesitate to include this in my list, because although Garuda is a singular personal Deva in Hinduism, in Buddhism Garudas are a race of anthropomorphic bird creatures. The Buddhist version has been transmitted to Japan almost completely intact. The association with fire seems to have been amplified to the point where the Karuras are capable of breathing fire. A notable difference between the two versions is that in Japan Karuras are sometimes depicted playing the flute. 
Brahma/Bonten: Bonten remains relatively unchanged from Buddhist Brahma. However, Buddhism in its rejection of a divine creator strips the Hindu Brahma of his universe-creating abilities and transforms him to the “king of the Realm of Forms.” It is said that Brahma descended from Heaven to teach the Buddha’s teachings to humans and bring them to enlightenment. In medieval Japan, Brahma was thought to rule over India (as Vishnu ruled China and Shiva ruled Japan) and created it’s brahma writing system. Joto’s “Commentary on the Treatise on the Lotus Sutra” contains an interesting variation of the Hindu myth of the creation of the Vedas. In both versions the four faces of Brahma expound the four Vedas, but in Joto’s version there is a fifth face atop Bahma’s head which preaches a fifth Veda. The fifth however is the most profound and difficult to understand, and it is not circulating in our world.
Prthivi/Jizo: This is a highly altered form of Prithvi. Bodhisattva Jizo is extremely popular all over the Buddhist world, including Japan. The “mother of all creatures” role she plays in the Vedic texts has been amplified into an all encompassing compassion for all beings. According to the mythology, she is currently capable of enlightenment but is waiting to leave the world until all living beings are saved. Her similarity to Avalokiteshvara/Kannon sometimes causes the two to be conflated in Japan. Prthivi worship fell out of fashion relatively quickly in India, so most of Jizo’s evolution took place in China. For more information click here.
Varuna/Suiten: A water deity, much like his Indian counterpart though his mount has been switched from a makara to a tortoise (not pictured.)  However, in one of his versions he seems to have switched into a female, and taken on characteristics very similar to Saraswati/Benzaiten. Suiten never gained much popularity in Japan, probably because it already had Suijin, a much better established Shinto water deity. 
Varuna and Indra/Raijin: Varuna and Indra, along with the Chinese deity Fengshe influenced the development of Raijin, the Japanese God of Thunder. He is depicted with circle of drums swirling around his upper body, which he beats to cause thunder. In Chinese myth him and his ally, Futen were demons who opposed Buddha, but were subjugated by him. Raijin is sometimes credited by the Japanese for causing the powerful storms, which destroyed the invading Mongolian fleet in 1274.  
Vayu/Futen: Guardian of the northwest. Vedic wind deity blended with the Taoist thunder deity Leigong, the and native Shinto deitiy Fujin. Usually depicted alongside Raijin.  His “bag of wind” belies his Shinto roots. 
Skanda/Idaten: Skanda is the Sanskrit name, but in India he is most commonly known as by his Tamil name, Murugan. In both locations he is the son of Shiva/Daijzaiten, and the brother of Ganesha/Kankiten. In an exclusively Japanese myth, Idaten becomes reincarnated as his brother’s wife in order to turn him away from evil. He is therefore often considered to be the female component in the double-Kangiten image. In that case, he is depicted with an elephant head to match Ganesha/Kankiten.  Normally depicted balancing a sword and in soldiers garb, he is a protector of Buddha’s teachings. In the Hindu version as well, he is a protective deity presiding over warfare. Like one of his father’s manifestastations (Daikoku-ten) he also serves as a kitchen deity.
Vishnu/Bichuten: In medieval times, Bichuten was thought to be the divine ruler of China, and the creator of the “Western barbarian script”, in other words the Kharoshthi script used to write Gandhari, the Prakrit dialect spoken in modern northwest Pakistan and Afghanistan. The Kharoshthi script had importance to the Japanese as a language in which many Buddhist texts were written, and translated from. Though Bichuten exists in the Buddhist sutras, images of him are rare or nonexistent. 
Vishnu/Ungyo: Ungyo is the closed mouthed “Benevolent King” guardian figure who stands at Japanese temple gates. He stands opposite his open mouthed associate, Vairocana/Agyo (who is a Buddha, not a Deva, and therefore does not appear on this list.) Unlike the calm aspect, which Vishnu normally holds, Ungyo maintains the appearance of a fierce warrior.
Lakshmi/Kichijoten: A goddess of fertility, luck, and beauty in both traditions, though she seems much more strongly associated with wealth in the Hindu tradition. Since the 16th century however, Saraswati/Benzaiten has largely supplanted her. In Hindu tradition she is the consort of Vishnu, but in Buddhist tradition her consort is Kubera/Bushamonten.
(S) Durga/ (S) Chandi/ (J) Juntei Kannon: The Vedic Goddess Durga has a form called Chandi, which is an adaptation of a pre-Vedic goddess of Bengal. This is the form, which was exported to Japan. There, she became one of the six manifestations of Avalokiteshvara/Kannon (the Bodhisattva of compassion) and is associated with human realm of reincarnation. Chandi has undergone other major changes, including usually being depicted as a male, and losing the fierce, warlike aspect she assumed in her Hindu form. 
Chandra/Gatten: The moon god, or ruler of the moon in Hinduism and Buddhism. Usually depicted alongside Surya/Nitten, the analogous sun deity. The gender has switched, so that he is usually depicted as female, and is referred to as “Lady Ruler of the Moon” in the Tendai tradition. 
Vishvakarma/Bishukatsuma: in Hinduism, he is the divine architect of the universe, and the patron deity of architects, builders and craftsmen. However, possibly because Buddhism rejects creator deities, Bishukatsuma’s tendencies towards architecture and large-scale engineering have been altered towards sculpture, carpentry, and arts.   
Agni/Katen: Fire deity who was extremely important in Vedic religion, as messages and offerings to the Gods were carried up through the sacrificial fire. He is important to the Shingon sect because a type of Vedic fire ceremony (called Havan or Homa) has been transmitted and modified by them (into the Goma ceremony). Through Shingon Buddhism Agni veneration also was adopted by the small, mystical sect called Shugendo, though their Goma ceremonies were bonfire sized.  
Hariti/Kishimojin: While not strictly a Hindu Deva, she was an Iranic Daeva, so I’m including her on this list. In my previous post I detailed a Buddhist myth in which she is a child eating yaksha who turned into a benevolent child guarding entity after meeting the Buddha. That still basically applies. Her depictions follow much closer to a goddess or a bodhisattva than a yaksha though. She symbolizes fertility, easy childbirth, and the protection of children. She is usually depicted with only one child, whereas in Indian iconography she is often crawling with children.
Hayagriva/Ba-to Kannon: Hayagriva, the horse headed incarnation of Vishnu exists in the Japanese Shingon school, but not as his own figure. He is one of the six manifestations of Avalokiteshvara/Kannon (the Bodhisattva of infinite compassion) and is associated with the animal realm of reincarnation. In Japanese depictions rather than having an actual horse’s head, he either wears a horse-head crown atop his normal human head, or rides a horse. The Buddhist version of Hayagriva is much more fierce than the Hindu version. in Japan he is called a “funnu” or angry deity known for destroying demons. The Hindu variant is purely a God of wisdom and knowledge.  Probably because of a pre-existing Shinto horse cult which was associated with the protection of roadways, Ba-to Kannon is also a road-protecting deity. Livestock owners also pray to him for the protection of horses and cattle. 
Acalanatha/Fudo: He is the Center deity of the Five Buddhas of Wisdom (another system of cardinal direction guardians.) He is very prominent in Shingon buddhism and is known for his incredibly fierce appearance and associations. His sword is for cutting through ignorance, and subduing non-believers and demons (often surrogates for desires or temptations in Buddhism.) His terrifying appearance is meant to scare people into accepting the Buddha’s teachings, and relatedly, he is a figure associated with religious instruction.  He also carries a rope, and has a third eye. In Shingon Buddhism he presides over the post-funeral memorial service. 
I’ve made this list as extensive as possible, but there are plenty of other Devas who are mentioned in the Buddhist sutras who probably have depictions. I know for a fact that Uma, and Indrani have Japanese counterparts. There are several other versions of Vishnu, which I couldn’t cover. I know of one depiction of Krishna, though I doubt he was worshipped. There are also figures like Marichi and Yamantaka, which I left out for reasons of their own. I also know that the rest of the Heavenly Kings, Bodhisattvas, Vidyadharas, yakshas, rakshasas, kumbhandas, nagas, makaras, ghandharvas and apsaras were also adopted into Japanese culture and mythology, but if I detailed all of them then this post would become even more completely unwieldy than it already is. If you really must investigate further, this website was incredibly useful to me: http://www.onmarkproductions.com/html/buddhism.shtml Seriously I owe a major debt of gratitude to that website for all the information and images they provided me. And by they I mean Mark Schumacher and whatever associates he may have I seriously love those guys.
I only cited these slides in an image credit, but if you are interested in this stuff, its a good resource: http://huntingtonarchive.osu.edu/resources/lectures/670/lect22.pdf
 Ibid 1, pages 167-169
 Suzuki, Teitaro. The Seven Gods of Bliss. Chicago: The Open Court Publishing Company, Open Court vol. xx1, published 1907. Converted to HTML in 2002 by Christopher M. Weimer: http://www.sacred-texts.com/journals/oc/ts-sgb.htm
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/daikoku.shtml
 Teeuwen, Mark. Rambelli, Fabio. Buddhas and Kami in Japan: Honji Suijaku as a combinatory paradigm. New York: RoutledgeCurzon, 2003. Heading title: “The Three Brothers: Creators of Different Writing Systems.” Google Book: http://tinyurl.com/ac65a4s
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/daikoku.shtml#sanmen
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/benzaiten.shtml#.UQwQQErBNbx
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/bishamonten.shtml
 Illes, Judika. The Encyclopedia of Spirits: The Ultimate Guide to the Magic of Fairies, Genies, Demons, Ghosts, Gods, and Goddesses. New York: HarperOne, 2009. Page 281. Google Book: http://tinyurl.com/az2ufwx
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/taishakuten.html
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/karura.shtml
 Ibid 6, Heading title: “The Third Link: From Tenjin to Mahevra)
 Ibid 6.
 Ibid 13, Page 125
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/28-bushu-kannon.shtml#wind-thunder
 ibid 13.
 Ibid 1.
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/kankiten-idaten-other-tenbu.html#idaten
 Ibid 6.
 Strauch, Ingo. The Bajaur collection: A new collection of Kharoṣṭhī manuscripts – A preliminary catalogue and survey – . 2008: http://www.geschkult.fu-berlin.de/e/indologie/bajaur/publication/strauch_2008_1_1.pdf
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/kichijouten.html
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/kannon.shtml#juntei
 Leighton, Taigen Daniel. Faces of Compassion: Classic Bodhisattva Archetypes and Their Modern Expression–an Introduction to Mahayana Buddhism. Boston: Wisdom Publications, 2012. Page 176. Google Book: http://tinyurl.com/acaoezj
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/nikko-gakko.shtml
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/nikko-gakko.shtml
 National Diet Library, Imperial Household Museum of Kyoto — Western-style Building from the Meiji Era –– http://www.ndl.go.jp/scenery/kansai/e/column/imperial_household_museum_of_kyoto.html
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/12-devas.shtml#katen
 Shugendo, Doctrines Costumes and Tools symbolisme: http://www.shugendo.fr/en/doctrines-costumes-and-tools-symbolisme
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/kariteimo.html
 Schumacher, Mark. Japanese Buddhist Statuary: http://www.onmarkproductions.com/html/kannon.shtml#batou