The big one for me was Morrowind. All I knew at the time was that I was hungry for an RPG, and I needed a new game for my Xbox. Morrowind killed two birds with one stone. I admit that at first I didn't really "understand" the game very much at all. I didn't really know what to do or where to go, so naturally I attacked a guy, and then everyone attacked me and it was just a mess. I was very put off by the game in the beginning. I forget just how exactly it happened, but at some point it "clicked" with me that Morrowind wasn't as much a "game" as it was an entire world, and from that point on I was continuously blown away by the game every time played it, and it went on to become my favorite game of all time.
A more recent example would be Darksiders. All I knew about it going in was that supposedly it was as if Zelda and God of War made a baby. I can't put my finger on it, but something about the game really turned me off initially, so I didn't get around to playing until earlier this year, but when I finally did play it, I really could not have been more impressed with it. The story and characters aren't especially deep, but literally everything else about the game is second to none. It is absolutely equal to the amazing games that it's often compared to, and many aspects it surpasses them.