Tales of Vesperia: I originally played the demo and absolutely hated it. I had no intention of buying it, but I needed a third game from Gamestop for one of their sales, and there was no other game even remotely interesting. As a result I decided to pick it up and was highly impressed by the results. Turns out, the part featured in the demo was probably the only truly terrible section of the game.
BlazBlue: I hate fighters. I absolutely hate them. I was sort of interested in BlazBlue because of its artwork, but I never expected it to be an actually good fighting game. It's the only one outside of the Smash Bros. games that I'm willing to play extensively.
Dark Souls: From my experience, games that are based around difficulty are a mixed bag. Some are horrible, but some are great. I expected Dark Souls to be the horrible type, but my curiosity couldn't keep me away from it forever. Man, when I got into that game, I had no clue how engrossing it would become or how fun failure could be. It's the primary reason I'm currently regretting not having my 360 right now.
Super Meat Boy: Pretty much the same experience as Dark Souls.
The Walking Dead: Honestly, the only reason I started playing it was because the first episode went free. Even then I really just wanted to point out all the flaws because I couldn't believe an adventure game about zombies could be as engrossing as people said it was. It turned out that it was one of the most compelling stories I've ever had the opportunity to follow, and I don't regret playing through all five episodes even if I lost some much-needed sleep that week.
Those are the ones from recent memory at least. Then again, I've started buying more games out of curiosity these last few years, not so much because I really wanted them. Surprisingly, this has helped me find quite a few enjoyable games and currently has a much higher success rate than I anticipated.