I find gaming very satisfying when you play long, in-depth campaigns where you get to really know your character, and find they go on an emotional development of their own that you don't always expect. Sometimes you find yourself also actually experiencing your character's emotions. I've ended up crying mess in a corner alongside one of the other players in the Dark Heresy game I'm in at times, such as when the GM decided to kill off the team's initial Inquisitor, who to his surprise we'd really taken a liking to. Even at this weekend's game several years of gaming down the line a reminder of Sloan turned the two of us left from that era of the game into blubbing messes. It's great fun, and when a real emotional reaction is evoked like that you get such a kick from it, if you're into character driven campaigns.
I've played in various systems, from White Wolf's Vampire games and Scion, to Legend of the Five Rings, Wheel of Time (the first campaign I was ever in), Shadowrun, D&D, Eberron (a D&D spin-off), Dark Heresy, Kult (very dark, very grim horror), and a number of other systems over the years.