Akira

Now you can watch the full movie free at youtube. It is a cult classic. Characters from this movie were even made into action figures by McFarlane toys and many have made replica bike from this movie.
The director Katsuhiro Ootomo is a graphic novel artist who created the graphic novel of the same tittle so needless to say, he wrote the whole story and designed everything in this movie. He hired majority of best animators in Japan so there were no full length animation movies made during the production of this film.

For the bike chase sequence, watch at 3:00mark.