Conan the Barbarian for NES. Picked it out for my 7th birthday way back in '92 from the video rental store. I chose poorly.
Not my first game, but the only one I can definitely say I've had the longest. I had to replace a bunch of stuff when I split games with my bro, and I lost maybe half-a-dozen nes games when I let my best friend's nephew borrow them when I was in high school (including my favorite nes game, Crystalis, which was a good memory of my father... really wish I still had that particular copy).