Like others have stated: mostly RPGs for me. Sometimes to try out new classes or races. Sometimes to check out different party combinations. Sometimes just for the hell of it. Games I've replayed more than once:

Baldur's Gate series
Icewind Dale series
Neverwinter Nights 1 series
Neverwinter Nights 2 series
Mass Effect series (although I've yet to play the third one)
Dragon Age:Origin
Eschalon series
Alpha Protocol
The Witcher
Temple of Elemental Evil
World of Goo

Finished Marvel Ultimate Alliance like 3 times in a row with a friend. Fun times.

Usually when I feel like returning and experiencing again one of my adventures games, especially the first two Simon the Sorcerer, the third Monkey Island, Loom and Goblins 3. I must have played them a few dozen times over the years.

I don't replay games much nowadays because I don't have as much free time as I used to. These are my most replayed games:

Vampire: The Masquerade - Bloodlines
XCOM Enemy Unknown
Mirror's Edge
Mass Effect series
Baldur's Gate series
Fallout New Vegas
Star Wars Knights of the Old Republic
Warcraft 3
Final Fantasy VIII
Resident Evil 3

For the RPGs, I sometimes try out other classes/party combinations, but I tend to stick with my favorites (Ventrue, elf ranger, etc.).

Certain flightsimulators and racesims I have always installed on my computer because the have an infinite replayability.
Other games I regularly come back to are Civilization IV, S.T.A.L.K.E.R., X-Wing, X-Wing Alliance, Freespace.
But there are a lot of games I have played more than once, NOLF 1+2, Red Faction, Half Life and also a lot that I want to play again.
Mostly games that offer little other than the story I play only once.
Of course there are even more games that I have barely touched because I can't keep up the interest playing them. =/

Torchlight. Because it's just fun (and I still don't have TL2 :p )

Gran Turismo 5.... I just can't stop collecting old cars.

Sonic All Star Racing Transformed. Seriously go get this game guys!

Minesweeper..... :p