I rarely complete the games I buy now, unless they are good enough to keep my interest right from the start. Last game I bought and completed was Alan Wake. Since then, I've tried to complete some old classics which are rated highly by many people, such as: STALKER, Mass Effect 1, Bioshock (tried many times before but I just lose interest), Far Cry 2 (spawning AI just frustrates me).
The last good games that I enjoyed and completed in the past year before alan wake were:
RAGE
Deus Ex: HR
BF3
Portal 1
Duke Nukem Forever
Granted some of those are your typical FPS game, but I do enjoy putting a game on and just having fun and not having to think too much about anything. Portal and Deus:HR are the last two semi-thought provoking games I played. Deus Ex was because of the story and Portal was for the puzzles. I don't mind a challenge as long as it is rewarding. A lot of games make me feel like I need to do a zillion things before the game actually gets better, and I just don't have time and patience to play through something I am really not enjoying to supposedly get to the better part of the game!
Games I really enjoyed in the past were:
HL series
GTA series
Quake series
First two COD games (although I did enjoy the later ones)
Medal of honour series
Deus Ex series
Tomb Raider series
Thief series
There are probably more, but I can't remember them all.