For me, it was Portal. It just showed up on my Steam account, I don’t remember buying it. I remember hearing something about it, a puzzle game where you have a gun that shoots portals, or something.
Well last night, after beating Witcher 2 I thought what the heck, I’ll try a level. Holy crap, is this a cool, smart and funny game. What are your surprise hits?
The two that I can think of offhand are Katamari Damacy, which is surprisingly fun despite sounding like the dumbest game idea in the universe, and Prince of Persia (the reboot), which I bought because it was on sale for something like $2.00 and turned out to be quite enjoyable.
Team Fortress 2.
Historically I’d hated online FPS, because I’m not too good with the twitchgaming. But I’d gotten the orange box, loved Portal, loved Ep 1 and was out of things to play. So I played TF2.
Holy shit, this game is hilarious! And especially on instant respawn maps, it’s very forgiving. Even when I sucked I was having fun. Now I’m hooked, and I’m not too bad at playing it 
Batman: Arkham Asylum
Not sure why I decided to give it a try but I am super glad I did. I thought it’d be some cheesy “license a big name and make money with little effort” thing but holy shit…game was fucking great!
I cannot wait for the next installment (I am going to go broke when it comes out as several games I am anxious to play will release around the same time…ah well).
Star Wars: Knights of the Old Republic. I bought it because it was literally the only new Mac game I could find at the time; I’d passed over it several times because hey, licensed property. One of the best RPGs I’ve ever played.
Mount & Blade. I’ve always been an unabashed graphics snob, but it’s one of the very few games produced now that quickly makes you forget about the vastly outdated graphics and problematic interface, just because you get to ride into combat with troops that actually follow you.
I bought Total Annihilation more or less to shut my best friend up after weeks of him telling me to buy it. To this day I love it.
I’m gonna go old school and mention a board game that I really love. Eurorails .
I suck at FPS as I can never seem to get the reticle to work without lots of flailing. So I was surprised personally how well Bioshock worked for me.
Before Need For Speed: Underground came out I thought the last few were kinda meh, but NFS:U was outstanding for its time. That’s the trend of the series, it goes from great to not-so-great (Carbon, Undercover) and then great again (Most Wanted and Hot Pursuit).
Mega Man Battle Network.
My mum bought it for me because she remembered I liked the NES series, and when I realized it was nowhere near a platform game, I was pissed off. Until I played it.
It is quite possible that I like this franchise more than the original. But not really.
Chrono Trigger. I tend to not enjoy JRPG turn based games at all. I found FF6 really monotonous, for example. The combat in CT is better though since it’s not all random encounters every 2 seconds. It has really good music and characters + a time travel plot.
Tales of Vesperia. I was expecting just a generic JRPG grind with a thin plot and silly characters to pass the time for a few hours. It was that, but 60 hours later I was still having fun :eek:
Another one I just thought of: Burnout.
Car games bore the piss out of me. My ex housemate used to play Gran Turismo and MY GOD IT WAS BORING.
I’m not sure why we picked up Burnout 2. But DAMN that’s a fun game. Awesome soundtracks on all of the Burnout games and mad fun all around.
Peggle. I got the demo somewhere (probably linked from here at the SDMB) and found it reasonably fun, but not enough to get the full game. Then when I got a newer iPod and went looking for games, it popped up again and I decided that I couldn’t pass it up for $10. I think it plays much better on the iPod than it does on the computer, and I have basically beaten the whole game twice (all the levels, all the challenges) at least on two different iPods. I’ve yet to figure out how it’s so addictive.
SSX 3. I even liked a bunch of the music, which I honestly didn’t expect given the character style.
Zuma, a marble puzzle game. Totally worth every MS point I spent on downloading it from Live.
I thought I’d like Plants Vs Zombies a bit, enough to try. I was surprised that I liked it enough to finish it.
There’s a card game called Fluxx I’d heard bad things about but I found it enjoyable when somebody broke it out one night.
Some people were surprised when I got into The Sims and I was one of them.
Here are two of mine:
The Sims 2. Decided to buy it on a whim because it was cheap and found myself instantly addicted. Played it for years and bought almost all the expansions. Not so much a fan of The Sims 3 though.
My story of Angry Birds was similar. It was free and I had heard a lot about it (this was after it was relatively popular but before it became a phenomenon). Boy howdy. Flash forward a few months and I have the Classic game, Seasons, Rio and a Bird-sized Monkey on my back.
Back when I first got my original xbox, I bought a game called armed and dangerous. Everything was totally off the wall with that game, I loved it.
Declan
Warriors, on xbox, my roommate picked it up and I laughed at him, we sat down to play and didn’t move until we beat it almost two days later. Then we went out and bought the movie.
Gladius also on xbox took me completely by surprise.
High School Drama: Varsity Edition is much better than I expected too.
Eternal Darkness, for Gamecube. I’m not normally into survival-horror games, but I played it at a friend’s house and was gripped by the storyline and general tone of the game. I eventually bought my own copy and went back and beat it 3 times to get the special ending. I’m still surprised at how much I like this game.