Online multiplayer games. I tend to only play one or two at a time. I might get sidetracked for a bit by a single player game but not for long. In order, I’ve gone from Left 4 Dead 2, to Team Fortress 2, to Starcraft 2, to Dota 2. Lots of 2’s.
An odd mention, but I frequently find myself going back to Crazy Taxi; It’s a strange choice since it offers virtually none of the ‘new experience’ or ‘story’ that usually drives replays for me. I suppose it’s just the fact that the game is fun to play. Go figure.
In “modern times”, Steam says I have 252 hours in Dragon Age: Origins (played through three times plus Awakenings and other DLC), closely followed by 250 hours in Team Fortress 2.
Older than that, I suspect Civ 2 and Medieval: Total War (the first) would dwarf either of them. But I also owned less games back then.
When I was younger, the games I used to replay most often were probably turn-based PC strategy games like Civilization (original) and Warlords (original), and later on Civilization 2, Alpha Centauri, Colonization, Warlords 3, and Heroes of Might & Magic (2 & 3).
The games that I replay the most nowadays are RPGs for the Xbox (or, more rarely, for the PC) where multiple run-throughs are required to experience all of the available character abilities or possible plotlines. Like Baldur’s Gate (original), SW: KOTOR, Fallout 3, Morrowind, Dragon Age (1 & 2) and Mass Effect (1 & 2). If a game is too frustrating, I’ll tend to give up too quickly (like Baldur’s Gate 2). Note that I probably start those types of games 3-5 times for each time I actually run through the whole thing!