Although I just entered two other raffles, I'd feel bad if I didn't toss my hat into this ring, too. But don't worry, good folks, I've got one of my own planned.
Without further ado, my all-time favorite non-Ninty game has to be Sonic the Hedgehog 3 + Sonic & Knuckles add-on. I was that kid who gobbled up Sonic 1, Sonic 2, 8 bit Sonic, 8 bit Sonic 2, even tried to hold down Sonic Spinball (I hadn't yet discovered the Crush games).
But man, did Sonic 3 just blow it all away. A lot of people like to rag on it, saying it's not as good as Sonic 2, and while I love Sonic 2, this third iteration just took all that was good and made it even better. The music was phenomenal, the stages absolutely memorable, the bonus stages both a treat and a challenge, and the size of both together tremendous. I thought they did the bubbles far smarter in this one, the graphics really wowed me, and the seamless transition from Sonic 3 to Sonic and Knuckles just flawless.
This was a great game. Despite the fact that the Turbo is hooked up right now (with Military Madness in), I may have to set it aside for a few moments to play through S3&K soon.