This is mine, too. I tried racing games as a kid and could never bring myself to finish one, so when my nephew insisted we play Burnout 3, I was really just indulging him.
Then I played a Road Rage event and that led to Burnout Paradise being the first game I bought for my 360. It’s my go-to for letting off steam after a crappy day. 
Another vote for “Portal”.
I’d bought “The Orange Box” back in late 2007, but ONLY for Half-Life 2, since the original HL was my all-time favorite game. I installed the full pack including TF2 & Portal. I played a little of each game but “Portal” just seemed confusing to me. I never advanced past the 2nd room, and after a couple of months everything was purged when I bought a new computer.
Fast-forward to summer 2011. I’m reading reviews about this great game being released called “Portal 2”, but everyone is careful to say that although great, it’s still not “Portal”. I love playing great games, but the completeist in me won’t let me play Portal 2 until I’ve finished the original Portal. I re-installed it, got the hang of it, and absolutely LOVED it! So much in fact, that I’ve played through it FIVE TIMES times since installing it last weekend!
I’m now downloading bonus maps and playing through them! 
If you haven’t yet, play through Portal with the commentary turned on, it’s pretty impressive how much care they put into making a great game.