Is The Joker a good fighter?

Okay I was never a big comics fan, but I always liked The Joker. He just emanates cool, and all the things he does are so illogical, but they work. I went to see the "Dark Knight" just to see Heath Ledger as him. In the movie, The Joker is portrayed as being a pretty good fighter, even against Batman. He fights dirty, but then again there is no such thing as a fair fight. I know that his portrayal in the comics varies, but is he normally portrayed a being good at hand-to-hand combat?