Me, I like the interpersonal roleplay. By that I mean the bits that come when you're just dealing with the details of each character's lives. Not plot, not driving home personal story lines, just dealing with the characters in and of themselves. For me, the best games are those where the characters develop real bonds to one another. Kinda like in Firefly, where the crew became a real family in the last few episodes. This doesn't mean I dislike the story, setting, or gameplay, but those usually come second for me.
So, how do you like to roleplay? What type of roleplay do you get the biggest kick out of? To be clear, saying that you love rolling dice and chopping kobolds in two is fine by me. So is saying that you could care less if your character lives or dies, as long as you have an internally consistent setting. I just want to know what you like.