It's actually somewhat hard to describe what I'm really looking for in a game. I think most of the complex issue is because for me the game is about the people I'm playing with, more than just the game itself. Having played everything from combat heavy strategic campaigns to significant roleplay heavy non-combat games, it really comes down to meeting people who I enjoy playing with, those who have a good time in good company.
I've been a roleplayer since the red box of AD+D I found at a yard sale for three dollars, nearly 20 years ago. Over time I found that I enjoyed creating the story as much as being part of it, so there's no difference to me whether I'm GM/DM/STing or playing as a character. I've played a vast amount of systems, from D+D to GURPS, to Rifts, to oWoD and NWoD. The series of recent campaigns I've been have been very involved; a nWoD/Hunter/Witchfinder variant run by a Doctor of Philosophy in an 18 person group, a roleplay heavy D+D 4e campaign where the players were challenged to create the history of the world as much as play in it, a combat heavy D+D 3.5e campaign designed to play from 1-20, and my own nWoD chronicle, based in current times but with links to history.