Good topic, straightforward and fun.
I wish I could be sure, but it's not easy to remember as far back as January. I know that I've played to completion:
Dark Souls - Three times, actually. I beat it last year, and couldn't resist trying some new builds and weapons, so I not only beat the game with 3 characters, but I also beat New Game+. Such a great game.
Bioshock - For probably the sixth or seventh time. One of my all-time favorites that I play at least once a year.
Bioshock 2 - For maybe the fifth time. I never understood why this game was a failure for so many fans. It's almost as good as the first if you ask me.
Bioshock: Infinite - Another replay, though this one I had only beaten once, just after it came out. I think I liked it even better the second time.
Batman: Arkham City - I started playing it last December, but beat it in January, and then played and beat it again.
Batman: Arkham Origins - This is the first one on the list that I've only beat once.
Alpha Protocol - Yahtzee's negative review actually made me interested to play this game, so I got it for four bucks. I'd say it certainly matched that investment.
Dragon Age II - For the third time. I will need to replay it and Origins in the next couple months I guess.
Mass Effect 1, 2, and 3 - My favorite game series in the world, that I play probably two or three times every year.
Pokemon Blue, and Pokemon Gold - I hadn't played either in several years, and I got the urge to play them again for the millionth-or-so time.
I have started a couple games that I haven't finished, like The Last of us, and Infamous, but I will probably finish them after I am done with Dead Space.