Akira was a tour de force that really highlighted how far in advance of other forms of animation anime was capable of going. However, it's not what really broke anime out of its niche market.
That honor, I'm afraid, goes to none other than Robotech.
At a time when American kids otherwise had G.I. Joe and the first iteration of My Little Pony to look forward to on mainstream television, Robotech broke in on early cable networks via the "UHF" stations which were usually unable to afford much in the way of quality programming. Unfettered by network censors, director Carl Macek was able to take three utterly unrelated anime programs, weave them into a single overarching plot, and present them to young American audiences in a way they could understand. It also broke away from the cliches that often made Japanese programming obtuse or even silly to Westerners (such as the cramped dubbing found in Speed Racer, Kimba, Battle Between the Planets or Gigantor).
Robotech, to those of us who were there when it arrived, simply blew everything else out of the water. It was popular enough to spawn a successful series of novels and merchandise, as well as a variety of games (including a knock-off that itself became very popular, Battletech).
Akira reached American audiences mainly through video outlets such as Blockbuster --- but it didn't stand there alone. It was stacked with those anime hits which had gone before, which had proven that a market for such video existed. Akira was like the third stage on a Saturn V rocket --- a critical part of the vessel enabling anime's flight, but it could not have gotten to where it was most useful without those stages which came before it.
