Characters I play tend to fall in one of three categories: (1) in-combat support, (2) non-combat skills, or (3) self-sufficient.
By far, the class I play most are rogues. I don't play them for the scoundrel bit, but typically because they're the class with the most access to abilities useful outside of combat.
Second-most are rangers and druids. I'm not a nature person, but I enjoy the self-sufficiency aspect of rangers (flavor-wise, not necessarily mechanically), and druids are interesting to me in that they have a wide range of spells and abilities. Again, both classes tend to have abilities that are useful outside of combat. The fact that I hate playing clerics made the druid my go-to class when I was put in the healer spot in 3.5 games.
Bards and warlords are fun because of the support aspect. I like the idea of playing a character whose main shtick is specifically to make everybody else better. I've played a smattering of artificers, as well, for much the same reason.
I also enjoy playing psionic characters - don't know why, just always liked the idea. I've rarely played a character whose sole shtick was psionics, though; one of my favorite characters is a noble with a few levels in a psionic class.
I'm pretty sure I've played at least one character of any class on the list, except maybe barbarian, just to give them all a try. Those five (six, if you count artificer) are definitely higher on the playcount, though.