I want and mean to finish every game I buy, but I do have a decent pile of shame right now, some of the games have been on it for years;
Okami on Wii - Got the game for my birthday a number of years ago, lost interest during the second hour of prologue/story
Fallout 3 - I got it for Christmas the year it came out, it's a game I've been wanting to play, but other games always get in the way
Resident Evil on Wii - I remember trying Resident Evil games and got annoyed with the controls. Then I played 4 on Wii and thought it was great, so I gave this one a try, turns out I still don't like the controls of the original games.
Fallout New Vegas - Thought buying this would give me motivation to finish Fallout 3, I was wrong, at least New Vegas only cost me $10
Zelda: Skyword Sword - Like Okami, the dense story turns me away, I don't remember so much reading and story in other Zeldas
Assassin's Creed 3 - I love the franchise, but this one isn't working for me, maybe it's the 6-7 hours I put in before I actually got the hidden blade. I might try to start playing this again soon though
Dishonored - I'm definitely going to start playing this soon, got it for Christmas, but got distracted by other games
Doom 3 BFG Edition - Same as Dishonored
Then there's games I want that 100% achievement record;
Assassin's Creed - Never got all the flags, at some point I start working on this, very much a backburner project
Dead Rising Off The Record - I have two non-multiplayer achievements to get the special diet one and 100,000 kills. Special Diet shouldn't be too bad, 100,000 kills, ugh...
Borderlands 1 and 2 - Really just a lot of little random achivements left, the biggest problem is going to be the raid bosses since I would much rather by myself
Bioshock Infinite - Well this I'll finish tonight, just have to track down one Voxophone and I'm done
I have made a deal with myself though, I can't buy a new game until I finish 2 games I already have.