Persona 4: Golden
I was hyped for this, and I was expecting a good game. But I wasn't expecting it to be THIS good. Many of the aspects of the game I thought I wouldn't like I ended up loving.
Final Fantasy VII
This is probably my easiest answer. I bought it at a boot fair with my step brother (first time meeting him) because it was 20p. I really wasn't expecting much, in fact I was expecting it to be POOR. But the next day I was hooked, and a few weeks later it became my favourite game of all time.
Tales of Vesperia
Similar story to Persona 4: Golden. I was hyped, I was expecting a good game and I spent a lot of money on it, but it still managed to greatly exceed my expectations. Possibly my favourite game of this generation.
Fallout 3
It was an impulse buy. I had recently gotten a PS3 and all my other friends had bought the game too. It also ended up being one of my favourite games of the generation.
Skyrim
I bought the game because it was cheap, I had pretty low expectations after playing Oblivion. On the 2nd day of playing I ended up logging 12 hours. Yeah, it was that good!