+1
John Cho, of Harold and Kumar, is the only Asian-American actor to have a leading role in a relatively "mainstream" movie in the recent past. He doesn't do martial arts or play a gangster in that film (I've only seen the first Harold and Kumar), which as you say is rare. He still adheres somewhat to stereotypes, though, as he is a meek, somewhat emasculated guy who has trouble talking to girls and can't stand up for himself to his jerk (white) co-workers. This changes at the end (spoiler alert?) as he develops, somewhat, as a character.
Cho was allowed to be more of a well-rounded lead character in Better Luck Tomorrow, which had a largely Asian-American cast and an Asian-American director, and actually received a fairly wide release (close to 400 theaters at its peak) thanks to a partnership with MTV. There was an interesting story when it came out in 2002 and was making the film festival rounds, that after the film during a Q&A, an audience member was upset that the film portrayed Asian-Americans in a negative light, because it was one of the few films to portray Asian-Americans at all. Then, Roger Ebert of all people stands up and says, Asian-Americans shouldn't be portrayed as saints; they should be portrayed as real, complicated people, without regard to what race they are. Only by being realistic characters and not stereotypes of caricatures of their race can they make headway to the mainstream (this is all paraphrasing, but that's the gist of it). Basically, Ebert destroyed that guy.
So to answer your question, no there aren't any Asian-American or Asian leading actors in Hollywood, in non-martial arts roles. Cho is in the Star Trek films as part of the ensemble, which makes him the most visible Asian actor in Hollywood, but as far as I know he hasn't been in a mainstream leading role other than the Harold and Kumar films. There are a lot of reasons for this, and I'm not sure if I'm qualified to go into a big explanation, but it comes down to what Hollywood thinks people will spend money on. Will people want to watch an Asian actor as the lead in a big budget film, like Dragonball, or should they cast a white actor with weird hair? Hollywood decided there was no way they could cast an Asian actor for a movie based on an Asian story, with Asian characters. And that was even for a movie with fighting and martial arts as a large part of it! They were okay with casting Asian actresses, though, because they are accepted in Hollywood as an exotic, desirable character type.
Anyway, the TV actors mentioned above, Steven Yuen from Walking Dead and Daniel Dae Kim from Lost and Hawaii Five-O, have played fairly interesting characters. Not the leads, obviously, but as part of strong ensemble casts. That seems to be the best Asian-American actors can hope for, at this point, but it's a positive step.