Well, not surprisingly, the game that's closest to my heart is definitely Sonic & Knuckles. That game really defined my childhood, as well as defined my tastes in gaming (Platformer nut here!).
Before I had the game, I would rent it every weekend and play it as often as I could, and each time I would get closer and closer to beating the game. Heck, I even remember the place where I recieved the game as a present on my birthday. I was so pumped to finally own the game, so of course I played it as soon as I could. When I finally beat it (took me forever to figure out that you had to hit the Master Emerald on the "final" Robotnik) there was a celebration at hand... until I found out that you didn't get the good ending unless you collected every single emerald. So off I went again, finding those pesky emeralds. 
So yeah, I own four versions of the game (Genesis, PC, GameCube, and DS) and I love the fact that I could play Sonic 2 and Sonic 3 with Knuckles thanks to the Lock-On Technology (sounded so futuristic at the time). I would go to Chemical Plant Zone and just climb the giant walls the whole time.
