Couldn't think of anything at first, then I started scrolling through the comments and saw several people saying Xenoblade. Had a "*facepalm* duh" moment.
I hardly knew anything about the game before playing it. I was following Operation Rainfall stuff, knew a little bit about each of the three games, thought they all sounded cool. Even then when I knew Xenoblade was considered the 'best' (or at least the most adamantly requested), I didn't read much more about it than the other two. I signed the petition, promising myself I'd buy all three games if they were ever localized. That in itself is unusual for me, I rarely buy games without doing a great deal of research on them beforehand, especially at full price. But all three were localized, and I bought them all. Xenoblade is probably the best chance I ever took on a game I knew so little about.
Another game that comes to mind is Mario Sunshine. I didn't play this one until some time in the past couple of years. I expected it to be really good but not too hot. First few Shines disappointed even those relatively low expectations. But I kept playing and the game kept getting better and better; by the time I finished I ranked it just a hair below Galaxy and 64. It's an absolutely great game with maybe a dozen or so Shines that just felt stupid. Also, the controls in Sunshine are the best-feeling controls in the series.
Oh shit, Dark Souls. I don't know what else to say about that, I didn't think I'd like Dark Souls and then I played it, and then I played it some more, and then I played it a lot more, and now hot damn I love this game.
inFamous might count? I guess I wasn't really surprised it was good, maybe I was just surprised that it appealed to me once I got into it. It was kind of a slow process though, the first inFamous didn't blow me away but I liked it. I also knew inFamous 2 was supposedly better, so when I started that one and it was indeed better I wasn't exactly surprised.
The first time I can remember going from "what even is this" straight to "holy shit this is the best" is Smash Bros Melee. My cousin gave it to me for Christmas '01. I'd never heard of Smash before, didn't know most of the characters in the game. For some reason I mained Samus for a long time even though I knew nothing of her or the Metroid series.
