When I was a kid I used to play through the few games I could afford multiple times. I guess I have completed Super Mario World at least 50 times. Other games would be Yoshi's Island, Donkey Kong Country 2 and The Magical Quest starring Mickey Mouse. I can also think of some N64 games, like Star Fox 64, GoldenEye and Perfect Dark.

When thinking about the games I've played through in recent years, only one game come to mind: RE 4.

Uncharted 3, god of war 3, uncharted 2, metal gear solid 4: 5 times each

FF7-10 oh so many times
pro evo more times than I can count

Limited to this gen:

Super Mario Galaxy
Dead Space
Dead Space 2
Fallout 3
Halo: Reach
Metal Gear Solid 4

Games I've only beaten at least 3 times.

Mario Bros(1-3) and World, and Donkey Kong Country games - Around 20 each.(educated guess)

Uncharted DF - 5 times
Resistance FoM - 4 times
Resistance 2 - 3 times
Ratchet and Clank Future ACiT - 3 times
inFamous - 3 times
Resident Evil 5 - maybe like 8 times (60hrs in campaign, ironically I don't really like it)
Resident Evil - 3 times (1 original, 2 remake)
Resident Evil 2 - 5 times
Resident Evil 4 - 7 times
Resident Evil 0 - 3 times
Dead Space - 3 times
Dark Souls - 3 times

Paper Mario 64 - 3 times
Yoshi Story - Like 8 times
Super Mario 64 - Like 5 times (from beginning no stars )
Super Mario Sunshine - 3 times
Cruisn USA - Like 10 times at least.

...cant think of all of them.

Let me preface this by saying I rarely replay games. I like them, enjoy them, finish them, and don't go back, with exceptions to only my all-time favorites:
Wing Commander 1 - Oh man, this one blew me away. It was so good. And one of few games where doing differently.... changes which systems you went to and the game ending! One of the early games where multiple play-throughs really paid off.
Wind Commander: Privateer - 2
Halo: CE (a couple times solo, and countless times in Co-Op. it was peerless, there's a reason it seems to be on half of these lists)
Mass Effect 1 and 2 - At least 3 for the first, on my second time for ME2.

FFIX - 10+ times, its like reading my favorite (picture) book (with sound).

Demon's Souls and Dark Souls - who knows how many times across different characters for different PvP builds.

FFXII - 3 times

FFX and FFVIII - 2 times

Kingdom Hearts 1/2 - 2 times

Everything else is too short to matter.

Metal Gear Solids all of them, even Portable Ops
Uncharted 2 a few too many times
Sonic the Hedghehog 2, too many times to count

Diablo and Diablo II, Titan Quest, Betrayal at Krondor, Baldur's Gate I and II, Crash Bandicoot games, Final Fantasy VII, Thief series, Deus ex, Gothic 2 and 3, Morrowind etc.
I tend to replay long games, mostly RPG's, the only exception to the genre I can think of right now is Half-Life and Half-Life 2 with episodes.
I just started Betrayal at Krondor and HL2 episodes again today.

First 2 Pokemon gens, literally so many times that I don't even want to think about it - I reckon I could literally quote every trainer phrase in that game, along with the pokemon they use and at what levels.