Neuromancer and Blade Runner/Do Androids Dream of Electric Sheep? are kind of givens, considering the genre, and the ending definitely reminded me of 2001: A Space Odyssey. I also thought I detected a bit of American comic book influence in there . . . maybe Alan Moore's Marvelman, but I'm not sure whether that would make sense chronologically.
You must keep in mind that the original manga was made in 1982, and was preceded by "Domu" from 1980 to 1982, which featured similar themes. So, Otomo worked in the same time as the first dystopic 80ies movies were made - Mad Max (1980), Blade runner (1982), Escape from L.A. (1982). So he was not inspired so much by that, but he said, he liked the movies of american new cinema like Easy Rider and Bonnie & Clyde. But some things are very japanese also, I mean, if you take some of the most succesful manga series and compare them, you get the impression the japanese comic artists are obsessed with super powers. But Otomo has more a indirect and complex approach to the theme and so "Akira" is not focused on the battle brawling common to so much japanese "Superhero"-comics - like Fist of the North Star for example, which was made in the same time.
A very late reply, but Cronenberg has to be mentioned. Tetsuo's transformation and mutation is straight out of Videodrome, so are some of his hallucinations