I like a good mix of Hack'n'Slash and RP. I enjoy playing with folks who have taken time to flesh out a decent character history, who do their best to stay in-character for the majority of the session and who enjoy making the world they play in as alive and "immersive" as possible. I like all that to be interspersed between exciting combats.
Also, it would be great if everyone at the table was committed to playing through a campaign in its entirety.
I've played too many games to list them all. My group that I usually game with has a bit of gamerADD - deciding to start a whole new game after only a few sessions of one game. This is good in that it gives exposure to a wide variety of systems, but sort of frustrating in that, just about the time you get into your character and the world and the story, you have to create an all new character/world/story.