Given 4 roles, in order of importance, I think I'm an Actor, Thinker, Instigator, and Powergamer.
For me roleplaying is all about the character, the starting point of every player, so I try to get into my character's head and try to approach every situation as they would.
For types of character, I tend to play smart-guy types, problem solvers - it fits with my own personality. That is not to say I have never played anything else, but it's my 'default' character, which I am most comfortable with.
As a player, I can be a bit impatient when it comes to everything but character interaction and well-thought out planning. I will prod the others to action, and try to get things moving; depending on the character I'm playing, this usually either means I try to push the group to a decision, or interrupt endless discussions by immediately taking whatever action my character feels is the best idea.
Lastly, I'm an optimizer. I like analyzing systems for the 'game of Charop' itself, but since I'm primarily an Actor, I tend to optimize according to my character concept. I also sometimes try to design characters from the point of the mechanics, seeing a class or build that I like and trying to think of a fitting personality for it. Either way usually gives me a character that is far from min-maxed, but quite well optimized as far as the concept allows.