What Makes a Character Great?

I’ve been thinking about characters lately, mostly about how to make them more compelling. So I asked: Who are my favorite fictional police detectives? I came up with Lucas Davenport (John Sanford’s Prey series) and April Woo (Leslie Glass). I thought I might find commonalities that attract me as a reader. Instead, I discovered that they are very different.

Davenport seems to have no family, no parents or siblings that he is connected to in any way. April Woo has parents who are very present in her life. Davenport has a lot of money and doesn’t need to work. Woo has money problems (mostly because of her parents). Davenport knows how to play the political game to get what he wants out of the department. Woo is incapable of playing politics and lacks social skills in general.

So why do I like both these characters? Perhaps because they are both independent and unconcerned with what others think of them. They are also very good at their jobs. But I’m not satisfied yet, and I’m still thinking about this. So who are your favorite characters and why do you like them so much?