Hmm, I'm trying to think what kind of characters I like, and, I'd say characters I can somewhat relate to, as in they aren't perfect, but have different flaws (an example is the Engelsfors trilogy where everyone in the main cast is broken in some way or other, and I just can't wait to read more about each and every one of them). Keep their lives a bit mysterious and reveal a part of it every now and then to keep the reader interested in them.
I am also a sucker for characters that are a bit eccentric and/or underdogs in some way or other. But I'm not sure if that makes them interesting, or just that I sympathise a bit more with them =)