Skyrim and Oblivion - probably played 100 odd hours but still haven't done the main story lines, done most of the guilds ones and side ones though.
Baldurs Gate 2 - this ones odd because it's probably my favourite game of all time but I never got around to finishing it. I did get up to the last area back in the day when I was focusing on the story but my pc died and I lost the save and haven't gotten around to doing it again.
Thief (new one) - it's the only current gen game I've bought and not finished off.
Phoenix Wright: trials and tribulations - I really enjoyed the first two but playing them one after another got me burnt out abit. Need to finish this so I can go on to apollo justice and dual destinys
It's pretty rare that I play a game and not finish it. I don't play as much as most of the people on here. Maybe three or four games a year, plus some downloadable stuff. There are the occasions when I get a game and just don't like it enough that it just don't get into it, which I don't really count. That's true of this most recent Shadow of Mordor game. And it was true of Watchdogs. It may be becoming true of The Evil Within, but I'm hoping not. A lot of it is time constraint.
But as for the last game I truely liked that I just flat didn't beat, it would be Skyrim. I got myself so caught up in the side quest stuff, I wound up just spending way to much time doing that stuff. I was at a point where I probably could've just walked through the remainder of the story, but I kept getting side tracked by nonsense, and eventually just didn't want to do it anymore. Somewhere there's still a mage librarian that would really appreciate it if I could find a rare book in some remote cave (that is there for no logical reason) and who will give me nothing for it.
Chrono Trigger - Spent 60 bucks on the cart a couple of years ago. Played close to 40% of it, never bothered saving it (just kept the console on) until a power outage put an end to that. Ended up selling the SNES collection after hacking my Wii to get every SNES game, but never picked it back up.
Ni No Kuni - Got it and loved it, but stopped playing when I got into the console version of Diablo 3.
Ninja Gaiden 3 (NES) - It took me months to take out the original, two days to take out the 2nd, but could never beat the third due to it being the first in the series to introduce true game overs.