In general, I'd say RPGs, although that is admittedly a pretty broad term, which can conceivably everything from Skyrim to Torchlight to Fallout to Terraria to Pokemon; "RPG" is basically just a catch-all term for any game where the emphasis is on some sort of character progression and allowing the player to express themselves through playstyle and/or story choices.
My favourite RPG is probably a toss-up between Fallout: New Vegas and Fallen London. They're both quite different in a lot of ways (one is a AAA open world action-RPG, the other is some sort of weird text adventure social game thing), but they both give me the things I really want out of an RPG; lots of choices, lots of things to discover, and lots of different ways to play. In both games, I inevitably feel like my character is more a product of my imagination rather than that of the writers, which is a really cool feeling to have even if it's only an illusion.