Interesting topic!
There's a specific type of character that I find really interesting, but I haven't really found a good outlet for in any of the stories I worked on, since it's a type that would be very annoying if it kept appearing in everything I did. Basically, I'm really interested in the notion of purity and innocence, and I really enjoy taking it to the logical extreme, where the qualities itself becomes a strength that cannot be overcome by anyone who doesn't harbor them. I'm talking about characters who essentially transcended humanity and risen above "mere mortals" to the point that dishonest, deceitful or plain villanous people can't even be in their presence without it taking some kind of toll on them.
Actually, I think I may have included a character like that in a story I worked on. There was a goddess who symbolized purity of mind and spirit, and she gathered followers who shared her views and principles, and then these people inherited some of her divine qualities. My protagonist enters her temple and is left in awe: she thinks to herself that, if their willpower could manifest itself physically, they would crush her in an instant. That kind of thing.
Other than that, I like making characters that share qualities of people whom I get along with best: open minded and non-judgemental. The type of people who are sympathetic, and think twice before coming to a hasty conclusion or saying something that would be grossly misinformed or just plain offensive. Those people rock.