Shadow of the Colossus and Okami.
Nevermind hearing that SotC was a great game, I was really anxious to play it since I first heard what it was about. For me, an action/adventure game consisting entirely of boss battles and no smaller enemies appealed directly to my sensibilities, so if anything, I went in with really high expectations, which is usually the setup for large disappointment. However, the game actually broke through my expectations, far surpassing them and leaving them in the dust.
I saw trailers for Okami when I worked at a video game store. I wouldn't have known about it otherwise, I'd imagine, but the trailer seemed to appeal to me - the art style was pleasing, and the gameplay mechanic was truly unique. I had also recently turned sour towards JRPGs, which was the genre I was initially anticipating the most when I first planned to buy a used PS2. I was utterly disappointed with what the PS2 promised me, but I was happily whiling away time on SotC right before Okami was released. I gave it a shot and it BLEW MY MIND.
To put things in perspective, I figured that God of War had all the makings of a game designed specifically to my tastes. But I did find it somewhat overrated and felt that it simply "pretty good." To be fair, it did keep me interested long enough for me to play it through to the end and the day will come that I will play through God of War, so I don't mean to imply that it's a bad game, by any means. But I felt it was "good" rather than "great," as far as my experience with it is concerned.