It's a toss up between a lot of different games.
I was obsessed with Sonic 3 & Knuckles as a kid, and played it so much while hunting for secrets that I became burnt out on it. Just in that first two-week winter break in 1994/1995, I think I beat the game 11 or 12 times? And I've replayed it every year or two since release, so we're talking, like, 30+ times I've beaten the game, start to finish.
Speaking of games I've played yearly, that's Donkey Kong Country 1 for me. I personally think DKC2 is still a better game, but it's also a lot longer and more complicated. I can finish DKC1 in just under two hours, and I usually get the urge to do so around Christmas (when I originally got the game, so it's a nostalgia thing). If you figure I've beaten this game every Christmas since 1995, that's a good 20+ times.
When I got my Saturn, NiGHTS: Into Dreams was short enough that I'd come home from school and beat the entire game in a single sitting, every day. If you play it right, you can finish NiGHTS with all A-ranks in under an hour. I don't know how many that actually adds up to, but it probably comes out to 30-40 times when you add in other times I've finished the game since then.
The same goes for Parappa the Rapper. By its very nature, that's a game that's about 45 minutes long, and when I moved off of NiGHTS, I'd instead come home from school and play all the way through Parappa, every single day. So, again, we're talking 30-40 times.
But the king is probably Sonic Adventure. When I first got that game for Dreamcast, all I had was a third-party memory card, and something about it caused Sonic Adventure to corrupt its save data pretty often. It seemed like every other time I'd boot the game up, my save file would be missing (and since it only effected Sonic Adventure, I never narrowed it down to being a problem with the VMU). What this meant was that any time I'd get the urge to replay Sonic Adventure (and you should know by now that I replay my games a lot), I'd have to start over from the beginning of the game.
This meant I probably had to restart Sonic Adventure around 10-20 times per year. And even after buying it on a platform that doesn't corrupt my save data every three days, I've replayed the game probably close to a dozen times or more since then. So I've probably finished Sonic Adventure somewhere in the realm of 65-100 times in my life.