Well, it's not like you HAVE to play it again and again. But if the game is good and you really like it, then if it offers a somewhat different experience upon a replay, that's certainly a point in its favor, IMO. Personally, I'd rather have a great game that I can play for 30 to 50 hours and then replay for that long again.
I think this is part of the replayability factor though.
While I have some games that were a chore to finish once, others were enjoyable enough to me that I don't hesitate to play them again and again. I realize some people look at their games as disposable one-shot commodities and there's nothing wrong with that, but others consider replayability a large part of the game's value.

I often replay my classics: The Dooms, The Quakes and Duke Nukem 3D. Recently I've been in a Max Payne frenzy.... :D
I'm not so fond of replaying adventure games as you already know the story and it doesn't have the same impact on you than the first time you play them (TLJ...).
I also love playing through Harvester several times because of the freedom and the awesomeness of the characters <3
Knytt & Knytt Stories, because of their so unique atmosphere.

Awesome games, finished Knytt Stories about 4 times now. Knytt actually reminded me of Another World. Also, I loved Within a Deep Forest, though it does not focus on atmosphere as much as Knytt does.

I have easily spent hundreds of hours on games like Fallout, Jagged Alliance 2 and X-Com. I replay RPG and strategy games mostly since they seem to offer the most variety. In most action/adventure games there's only one or two paths.

I don't usually replay many games at all.
The games I have replayed have been:
Wasteland
NWN 1
Diablo 2
Dungeon Siege 2
Games I would like to replay:
Bioshock
Gun (don't own this one anymore unfortunately)
Wasteland (ditto)
and that's the extent of games I have or want to reaquire and have played through once and want to play through again.

Civilization 4 - addictive game
Oblivion i play so far then get bored then restart over ad over
Neverwinter nights 2 - enjoyable game

I replay kotor games. once every half year or so since the release (although haven't touched number two in a year. waiting for RP)
Transport tycoon. play it like crazy, a year or two break, repeat. been doing it since nineteen ninety five with break in 2000 to 2005 (lost the game)
Fallout 2. Play it. break. Play it again.

Let's see...
Civilization 4
Settlers 2 and 10th anniversary edition
Latter exclusively in "sandbox" mode, meaning just building an empire on the biggest meanest piece of rock. The former sometimes in sandbox, other times in "lets conquer all" mode.
Test Drive Unlimited
Again, sandbox-mode, meaning just cruising around in my favourite car.
F.E.A.R. & expansions
I love the game, especially the horror moments.
Freespace I & II
They are still the best space-sim out there, better yet, there are mods and that full engine rewrite.
Morrowind & Oblivion
I'd rather say that I never actually finished playing them instead of many replays.
Fahrenheit
I like the story, the setting, the realization, the quests.
Max Payne 1&2
The very best noir on PC. That and a very good shooter amongst other things.
The Longest Journey & Dreamfall
Yeah, another adventure game. These are my personal favourites.

Heh, I finished Half-life: Episode one at least a dozen times :D The game is as long as two average movies, so it's a good way to kill an afternoon :D
Well, I finished all half-life games several times.
Fallouts. That doesn't need commentary :D
Morrowind - I always discover something new. Fantastic game...
System Shock - I've finished first one at least five times, second one three times.
Fahrenheit, just look at nagi's post :D
The Longest Journey. Cause it's awesome.

For me, the most game I replayed was Oblivion. Once I'd figured out which stats choices where good I got hooked, then when I was starting to get board the modding community stepped in and lifted me back up.
If you haven't yet installed these essietial mods go get 'em, they make the game lovely:
Quals Texture Pack 3 (+ patch 1.3)
Unofficial Oblivion Patch 3.2 (also for shivering isles and dlcs)
DarNified UI 1.3.1
Shivering Isles (yes, this 'dlc' is acutaly worth the money)
Oscaros Oblivion Overhaul
I could go on.....

1. Civilization in all of its iterations, obviously
2. X-COM: UFO Defense
3. Master of Orion (only the first part, the rest were never nearly as good)
4. The Monkey Island series - can't get enough!
5. Secret Weapons over Normandy - replay it every six months or so, there's simply something fun about the way you can wipe out half of Wehrmacht in one airplane
6. Combat Flight Simulator 3 - but there's a lot of fun to be had getting pounded by antique Greek fighters in MedAirWar or runnig recce missions in a Me 440 over England

If I had to choose one game that I know would please me for all of eternity, it would be X-COM Terror from the Deep. Must've played a million times. I even started imagining and writing the story for my latest game as I play :) (It's more fun than it sounds)
Other games I replay a lot are:
Diablo 2
Fallout 2
Baldur's Gate 2

I have to go for the HalfLife 2 series: Played HalfLife 2, Episode 1 & Episode 2 on each of the difficulty levels with Episode 2 I worked on getting all of the achievements as well.
Portal: Short and sweet and played through about 4 or 5 times now.
KOTOR: Played through a few times before I lent it to a friend.
KOTOR2: Will be played again once the restoration project is released. Sounds like it'll become almost a new game.
Longest Journey & Dreamfall: Great games and enjoyed every minute playing them, so did it a few more times.
System Shock 2: Completed a few times, still scares the hell out of me each time.

I keep going back to Oblivion because great mods keep coming out with another dozen quests or so that get great write ups!

A true thread for the economic crisis.
Fallout series, for sure.
Jagged Alliance 2. I picked this up years after release, and I'm still playing it.
MGS3- not sure what it is, maybe the story, the setting, the characters, the CQC.
Kane & Lynch. *hides*
Urban Reign.
Civ 4
Betrayal at Krondor
Virtua Fighter 4/5
Persona 3
Max Payne series.
Full Throttle.
I'm excluding online multiplayer because that list would be even longer . . .