I'm gonna have to break this down by system:
360: Dead Rising was the first game I played this generation and felt that I was getting an experience I hadn't had before, chalk that up to the unique gameplay mechanics or the fact that I had some many zombies on my screen. It was mind blowing!. Following that the first Gears of War was the first game that made me appreciate paying for Live, playing co-op with someone randomly that didn't want to grief me probably helped. Plus the game looked stunning on my big screen. Plus, it was the 360 game I liked enough to bring over to my friends' places so they could see it and play it in person.
PS3: MGS4, it was exactly what I wanted from a next gen follow-up to one of my favorite franchises. It was the reason I picked up a PS3 and it was worth it.
Wii: Super Mario Galaxy because it gave me the same feeling I had when I booted up Mario 64 in middle school. And Skyward Sword because it sold me on the WiiMotion+