This is a tough one for me...
OK, at the risk of sounding like an Uplink fanboy, I have to say that it was one of those games that I did not expect to fall in love with. First of all, the game has no visible action, you have to type A LOT and quickly; those two points alone are enough to drive off the average gamer of the XBAWKS/PRAYSTATION3000 generation. I tried out the game and 6 hours later I have found one of those digital crack games I love.
The Guild is another game I really knew nothing about but fell head over digital heels in love with. THe only way I found out about it was through GOG and the recommendations of other members.
Space Rangers 2: I picked this up at a Gamestop simply because of the title and the box cover and the cheap price ($19.99). It also included the original Space Rangers along with a poster. But the best surprise was the game itself. Who knew that piloting a little ship around in turn based fashion, going through text adventures with really strange choices could prove to be so much fun?

rock paper scissors doesn't make sense?
if that's the case, I do not recommend you play Pokemon, ever.

Ditto Drakensang. I'm shocked by how good Drakensang is and how little press it's gotten. I think it's like a German/Dark Eye version of NWN.
Also, World of Goo. Really good game that came out of nowhere for me.

Good topic!
Mount & Blade - I'd read raves about it on various forums, then grabbed it when Gamersgate had it marked down by 70% or something like that. I don't think I played another game for the better part of a month after that purchase, and I still play it on a regular basis.
Armageddon Empires - Another one I'd read forum raves about. Looked like a neat idea, so I pulled the trigger...and again, it basically dominated my game playing for quite some time, and still gets played today.
AI War : Fleet Command - Sounded kind of interesting, but didn't look all that fantastic. I grabbed it anyway on the recommendation of a friend...what a blast!
Batman : Arkham Asylum - As others have said, I wasn't expecting greatness...then the reviews started coming in. I decided to buy, and it might be my favorite game of 2009.
Tropico - I had no idea what to really expect from this game back in the day. What I got was one of my favorite games of all time.
Madballs in Babo : Invasion - Grabbed this during Steam's Thanksgiving sale because it was $2. Ended up with a surprisingly fun multiplayer shooter.
Civilization IV : Colonization - I had not heard good things about this remake. Then I picked up the Civ IV Complete Collection and decided to give it (and the patch that had recently been released) a try. Very good little game that I need to spend more time with.

No swinging a sword costing Chi Energy makes no sense.

Spellforce Series:
"RTS / RPG mix ? what kind of a mess is that ? Can that even work?"
Those were pretty much my thoughts when i started looking into the Spellforce series. I wasn't expecting, well, anything to be honest. I'm certainly glad i did gave them a chance because between Spellforce Platinum and Spellforce2 Gold i had more hours of fun than i could count, and that's a lot cause i can count pretty high. [Bonus points for identifying the 'hidden' quote in this paragraph.]
URU CC:
I wasn't expecting much. For one after having played Myst 1 to 5 before even considering touching URU, i wasn't looking forward to play something that could potencially tarnish my perception of the Myst/D'ni universe. Also, the different timeline and the idea of the DRC and other explorers messing with the Ages was putting me off for some reason. Finally i caved in (no pun intended), and gave URU CC a shot. It went directly to number 2 in my all time favourite's list (Riven is and always will be number one), so yeah, very pleasant surprise.
DAO:
I knew i was going to enjoy it, but damn, i never dreamed i would enjoy it this much. I can't stop playing this damn game, i'm enthralled. I've probably buried more than 200 hours on this one already.

That's why this game is officially banned from my PC at least until winter break. Or summer break, to be on the safe side ;)

Smart move, i almost wish i had done the same. Oh well, too late now ;)

You will have a chance to avoid such mistake when ME2 comes ;)

Mega Man Legends would be my first major surprise. I gave it a try years ago and barely got 5 minutes into before giving up....and then a couple years ago I tried it again and just found the whole thing to be a blast. Very fun and endearing. A game I was sad to see end.

We'll see...
While i tend to find a couple of new mistakes to make every day, sometimes i end up making 'old' ones aswell ;)

Fallout. Got it as a cristmas present in -97 or -98 from my sister. I looked at the box and were like: Meh. Then I went and tested it. And tested it. On evening of 25th, after some 24 hours of post nuclear adventure I went to sleep very happy.

Beyond Good & Evil - I wasn't exactly that blown away by the demo but I got it on GOG in their two for one Ubisoft sale. It certainly surprised me how good it really was.
Plants vs Zombies - I've got nothing against casual games. But few take up as much of my free time as this one already has.
Borderlands - Okay, I was expecting it to be fairly good. At least in co-op. But nowhere near as good as it actually is. What surprises me most is how well balanced it is. Which is make or break for action RPGs, first person or otherwise. It also has Claptrap. Who should have his own game series and talk show if there's any justice in the world.

Games that surprised me at how good they were:
UFO: Aftermath - One of the first PC games I ever got, was blown away by how much I enjoyed it. Turns out it's the perfect game for me, Aftershock got better but Afterlight was a step backward with cartooney looks. Still, was in shock and awe for weeks from Aftermath.
Plants vs Zombies - This was a game I 'aquired' to try first because I thought it would be a dumbed down casual game. Bought it a day later, didn't regret it and yet that was dark side of the moon kind of difference to my first impression.
Total Annihilation - Deserves a huge mention. This is the first game I ever bought for PC. Found it at Target for $10. WHOA is all that went through my mind. Apparently I'm spoiled on hardcore strategy games because after this I thought all RTS's were awesome, well Command and Conquer just never stood up against TA back in the 90's, especially with the now defunct TAUCP (TA Unit Compilation Pack) with hundreds of custom units that rock! Endless waste of my youth, oh the memories. And all started by randomly seeing it on a shelf for $10 at Target while getting toothpaste.