Not too many games out there that I don't finish but here's few:
Sherlock Holmes: The Awakened. I lost interest towards it, I really can't explain why. It just was far from what I expected.
Ankh: Another rare piece of adventure game that I gave up early quick. Silly puzzles and poor and annoying humor probably turned me off so quick.
Final Fantasy 12! Don't get me wrong, I intend to finish this game. I'm a huge Final Fantasy fan. I really don't know why I have stopped on certain part, but I just have. I will finish it though so not exactly given up...but it's been over 8 months since I touched the game. By the way, main character Vaan is extremely annoying in FF12.
Black - this first person shooter on PS2. Not really bad game either, but it gets old and boring quick. Levels feels too similar.
I saw Dragon Quest 8 mentioned on this topic...I thought the game was brilliant, with a nice touch of humor too.
One of the best console RPG's ever.