Bill Maher is an atypical comic in that he's a public person as well. He isn't trying to play the part of a comic, and nothing more, or to play several discrete roles, and that's it. He's rather open to be engaged on anything. On his show he invites people whom apparently he respects a lot, but sometimes it really gets into a heated argument, they don't shy away from it. There is a lot of authenticity about him, less theater. And rather than a performer, he's more just about talking his mind.
So by that he is a rather well rounded character, which I think helps him as a stand-up. And above all, he's very good at telling a story. And that's what he does on stage too, he tells stories in a very relaxed and natural way, it really doesn't seem scripted. They are funny, but they aren't really sound bites either, they aren't manufactured to be funny word-for-word, it's the content that counts. And that's a different way of telling a joke than comics usually do, because they put every effort into wording it best. And they do that because they don't have the wealth of material that Maher does, or at least it appears so. He can easily go off on a little tangent, be funny, then return to where he was and continue with ease. He has that kind of coherence and clarity that not many people have.
But the funniest thing about him is that he's not really trying to be funny on purpose. The stories he tells are funny, but they aren't really jokes, they are just stories, presumably true most of them too. He's not really playing for laughs, it seems, because what he has to say is funny enough. And that's pretty confusing, cause you can't quite figure out how it works.
Maybe you shouldn't analyze it then :D