Woody Allen is equally famous as an actor, writer and director. He also had a career as a stand-up comedian, but this is a long time ago and probably not what he is remembered for.
Older people or serious film fans will always remember Allen's typical neurotic persona when he acted in films like Annie Hall, Sleeper and Hannah and Her Sisters. He also directed and wrote the screenplays (sometimes together with Marshall Brickman) for these films, and another thing he is famous for is his very high level of involvement in so many projects - ie it is, or used to be, quite usual for him to write, direct and star in the same movie.
Less known movies that still have a cult following include The Purple Rose of Cairo, which he didn't actually appear in, or Everything you Always Wanted to Know...
Allen has been less high profile in recent years, but in 2012 his screenplay for Midnight in Paris won an Oscar.