What games did you finish multiple times?

Errr, I honestly can't remember...

BioShock Infinite is the first game I've completed twice back-to-back since KotoR 2. But I've replayed tons of other games. GTA: Vice City is the game I've beaten the most. Though I've beaten FF 7 and 10 multiple times and nearly beaten 8 (in addition to my 1 completion) probably 2 or 3 times.

Legacy of Kain , Soul Reaver 1 , Soul Reaver 2. i finished them around 7 times or 8 times... My favorite games from Childhood.

I replayed a lot of games but the one I replayed the most is Final Fantasy IX. At the begining when I got the game I finished it weekly but now its my "tradition" to finish it at least once a year. I have finished it more than 50 times now. I should get into speedrunning it or something.

Ratchet & Clank 3.

Doom 1 / 2
Assassin's Creed
Call of Juarez: Gunslinger
Grand Theft Auto 3 / VC / SA / IV
Half-Life 2 / Episodes
Limbo
Max Payne Trilogy
Mirror's Edge
Portal 1 / 2
Prince of Persia 1 / 2 / 3 / 2008 / FS
Rayman 1 / 2
Splinter Cell: DA / C

I played many games multiple times. For example Mass Effect trilogy, Deus Ex: Human Revolution, Oblivion, Gothic 2, Half-Life 2, Simcity, The Sims 2 (can be finished?), Star Trek: Bridge Commander, Star Trek: Armada 2, Star Wars: Jedi Academy, SW: Kotor, Pirates, Civilization 5, Total Annihilation, Red Alerd 2, SW: The Old Republic, SW: Empire at War + FoC, Overlord I & II, X-COM: EU, SW: Force Unleashed, Need for Speed: Underground 2, Doom, Wolfenstein 3D etc.

And my personal best Star Wars: KotOR 2 finished 14 times. I love that game.

Super Mario RPG, Mario & Luigi Superstar Saga, The Legend of Zelda: The Minish Cap

Mafia 2, Half-Life 2, HL2:EP1&2, Portal 2, COD:1&2

Bastion
Both Portals
Little Inferno
Mark of the Ninja
and others that I don't remember now :)

Half-Life games, Starcraft games, The Longest Journey, Dreamfall, Syberia games, Still Life games, Max Payne games, Prince of Persia games, Doom 3, Vampire: The Masquerade - Bloodlines, The Sufferering games and probably a lot more I don't remember right now.

Beyond Good & Evil, Botanicula, Chzo Mythos series (free downloads: 5 Days a Stranger, Trilby's Notes, 7 Days a Skeptic, 6 Days a Sacrifice), Eternal Darkness: Sanity's Requiem (Gamecube), Legend of Zelda series (but specifically A Link to the Past (SNES) and Ocarina of Time), Machinarium, Mega Man X (SNES), Prince of Persia Sands trilogy (Sands of Time, Warrior Within, Two Thrones), Saira, probably more that I'll think of later.

Games I haven't completed a 2nd time through yet but that are very much worth it: An Untitled Story (free download), Aquaria, Aztaka, Back to the Future: The Game, Ben There Dan That, Breath of Fire (SNES), The Cat Lady, Crystalis (NES), Driftmoon (mods too), Skies of Arcadia Legends (Gamecube), Thomas Was Alone, Treasure Adventure Game (free download), VVVVVV, The Whispered World, Within a Deep Forest (free download).

Honorable Mentions (I have completed them for the first time yet but they're still very good): Antichamber, Auditorium, Blocks That Matter, Cave Story+, The Dream Machine (finished the chapters I own so far, 1-3), Fez, La-Mulana (remake version), Phantasmaburbia, Plants vs Zombies, The Real Texas, SpaceChem, Splice, Stacking, UnEpic, World of Goo.

Half-Life 2 + episodes, CoD4, some of Serious Sam games, Mafia, StarWars: JK2:JO, GTA:VC and SA.
And the recent game I finished 3 times was The Witcher 2 (went for easy, normal, insane difficulty). :>

The walking Dead by TellTale

Mafia II great game with one of the best Storys

Uncharted (all 3 games)
God Of War (all 6 games)
Medal of Honor
Battlefield 3
Killzone 3
Arkham Asylum
Arkham City
Gears of War(all 3 games)
Need for speed (Most Wanted, Underground, Hot Pursuit, Rivals, Run and may be more)
These are what I can remember right away. Played all these on Consoles

Bastion

Half-Life 2, five times maybe

mafia 2
sleeping dogs
and DOTA

I've played many games twice mostly for hardest difficulty achievement so those don't count. Games I've finished 3+ are these: GTA: Vice City and GTA: San Andreas.

I've played a lot of game, but not so much replay. I think the list should be something like this :
Old Mario Bros
Pokemon (1st and 2nd Gen)
Diddy kong racing on N64
All Jedi Knight Serie
Mirror's Edge (who's the game i've replayed the most with at least 15 replay ^^)
Guild Wars 1
Morrowind
Age of Mythology
and maybe more but nothing i remember now ^^

Sengoku Rance,
Yep finished multiple time...

more than five times: Arcanum, Fallout 1 & 2, BG 1 & 2, Civilization (pick your number, I played all of them, but mostly SMAC), Diablo II, Sword of the Stars: the Pit

less than 5 times (but more than twice otherwise that list would be far to long): Icewind Dale (but only first one, as I've beaten second only once), Half-life (first one that is), Homeworld, System Shock 2, Master of Orion 3 (yes, the THIRD), Majesty, TW: Rome 1 and Medieval 2, Age of Empires 1 & 2

plus bunch of titles from my Amiga and NES times