I am wondering if anyone else keeps playing a game, and keeps coming back to it even though you never win/beat it.

Minesweeper

I never managed to beat Half Life. The first time around it crashed repeatedly at the same point in the game, after repeated installations and patches. The second time around, on a newer PC, it crashed repeatedly at a different place, after repeated installations and patches. I gave up on it even though it's supposed to be a fantastic game. Not so fantastic when you reach a game-killing bug less than 20% through the game.
I don't think I've ever finished any of the Baldur's Gate games. I can never win the final boss battles so I'm doing something wrong over and over again. I probably don't use enough magic.

I've never finished Starcraft Broodwar. Got stuck on that Zerg mission where you have templars working for you and you need them to kill the overmind that the terrans are using. They always attack from so many sides and you start with so few minerals, I just can't beat it. My brother did mange to beat it, but he never managed to beat the last mission, where you get attacked by three different forces.
I still play Starcrfat, but the campaign has been effectively stuck there for ages.

A Nintendo DS game : Nanostray (shoot'em up).

I've played to just before the end of both Dead Space and Turok (2008) a couple times each and then always get distracted. Then 6 months later I decide to finally finish them but I start over.
Arg.
Dragon Age is a game I can't finish right now, it is too much of a time suck and I keep being distracted by new releases.

Most of them. I think I've finished about a quarter of the games i've bought.

Sinse I started playing one single player game at a time till completion only 2 games have been unfinished that I've started many times. Final Liberation and severance blade of darkness. Severance because I always get stuck at some flaming skeleton boss get annoyed at it, think I'll try some other time and never do.
Final Liberation I conquer about half the planet and then get distracted by other things. The amount of bugs that make the game crash don't help either. Nothing more annoying then having a huge fight for 4 hours and then the game crashes you have to redo it all.

PSH you guys are pathetic. This is my current list of games I purchased that I couldn't get into and never beat, or barely even started:
Infinite Undiscovery
Last Remnant
Tales of Vesperia (went on a JRPG craze)
Command and Conquer 3 (Yet i beat kanes wrath :/ )
Shadow of Rome
The Club (played it once... bought it 3 months ago)
Riddick Dark Athena and Butcher Bay (love the games... just can't play very far before doing something else)
Prince of Persia (bad game... BAD)
Kane and Lynch (ugh)
Hers the PC game section:
GOGs:
Fallout (im close too beating it)
Fallout 2 (didn't get past the first dungeon)
Blake Stone
Evil Genius (working on it...)
PC:
The Movies (never got a complete playthrough)
Diablo
Tiberian Sun (love C&C)
Medieval 2 expansion
Civ 4 (bought it and hardly played it... odd seeing how much I love civ and love that game)
Morrowind (Love the game, can't get into it...)
KOTOR (Been at the area before the last boss since the game came out)
KOTOR 2 (Ah crap I forgot about that one)
Neverwinter Nights (I really want to play some more of this...)
Titan Quest (actually i did beat this...)
Dungeon Keeper 2 (DRAT)
Sid Myers Pirates! (Got so close to the end...)
And I beat ALLOT of games...

Half Life always crashes for me at around the point you get the crowbar at an encounter with a headcrab. Always. But after getting past that crash (which may take several attempts) the rest of the game is fully playable.
Although there are apparently several more bugs in the Steam based versions and I have never been able to finish it when run from Steam. But the retail disc versions I have play ok asides from that one bug.
Personally, I've never completed a GTA game. I have far more fun with the sandbox elements and find most of the missions in the games to be far less enjoyable, so I just play the bare minimum to open up the whole world and then forget the story line completely.

I rarely finish any games that aren't FPS games. FPS games tend to be short and concentrated enough that I can burn through them before any problems, distractions or annoyances arise.
Don't think I've finished an RTS since Warcraft 2.
But I rarely go back to games that I get bored of, so that list is much shorter:
Daggerfall (Bought, got fed up of bugs, returned. Bought again next month, got fed up of bugs. Returned. Bought again next year, applied community patch, played a fair bit. Got fed up of bugs. Gave up).
Morrowind (Played on and off for about 2 years, without ever getting anywhere at all on the main story. Had fun pottering around, exploring and stuff. Ported progress across from at least 2 pcs, but when my laptop died last year I decided that if i reinstalled it then I'd never play any other games, so i decided to go cold turkey).
Tie Fighter (One of my all time favourite games, and I love it dearly, but there are SO MANY missions, and some of them require very precise timing. I played about 75% back in DOS on the collector's edition. Then I played about the same 75% again when I bought the windows upgrade. Plus I've gone back to it many times, but I keep losing my savegames and having to start from scratch).
Can't think of any others I haven't completed but keep trying... though right now I have a craving for Shogun Total War for some reason.

Street Fighter IV at the moment. Even though I haven't tried that hard anyway....
Syndicate - American Revolt data disk. Yes, I still have to complete this fucking beast....

I never finished the original StarCraft. I got stuck on a Protoss mission where you had 2 or 3 other Protoss factions against you, and they kept attacking in wave after wave, never giving me time to build up anything.

If I was to list the amount of unfinished games I have at the moment ... I think it would crash the database. Probably beyond repair.
I just registered on backloggery, and have all my PC games up so far. You can take a look there:
http://backloggery.com/main.php?user=stonebro

Mass Effect