Soul Calibur II. I usually eschew fighting games, save Smash, but a friend of mine wanted to play it, so we rented it for my GC. 2 1/2 years later, my friends and I have SC II-IV, and it's our most-played game as a group after Smash. Still don't like non-Smash 2D fighting games, but SC clicked. Maybe it's the 3D aspect, or that it's with weapons and is bloodless, or just that I've played so much of it.
Tales of Symphonia. I've never been that much of an RPG gamer except Pokemon, and that's a special case if ever there was one. But when my (same) friend got this and played it, I just had to get into it as well, and now it's one of my absolute favorites.
Age of Empires II. My friends at college wanted a game we all could play on our dorm's network together, and they'd all played this except me. I had to learn it and get into it, and I was hesitant, but it turned out to be awesome.