I don't know if I can specifically put these in favourite order, but here's my top 10 in no particular order (actually, alphabetical). I think I'm basing this more on how many times I replayed the game and sentimentality more than anything. My problem is this seems to be my top 10 for today. Next week, I might have an entirely different opinion. I'm odd that way...
GoldenEye 007 - The only first person shooter I ever got into. I'm a huge James Bond fan, and I didn't know that this game was generating non-Bond fan buzz before buying it. I was clueless as to why it took me weeks to track down a copy. Combine great graphics with memorable Bond music (moreso than the film!) and outstanding gameplay and this one was a hit. The cheats and multiplayer had me coming back many, MANY times.
Legend of Zelda: A Link to the Past - I never owned it, but I borrowed it multiple times from various friends. The sprite graphics are some of my favourite from the SNES, and the music is just terrific. I couldn't get enough to combing Hyrule for any secrets I could find. This one kept me company through a bout of sickness as well. It made the time to recovery fly.
Legend of Zelda: Ocarina of Time - I actually wasn't sure if I'd put this one in here, but it just made it in. So if I was numbering them, this would be 10. I love the game, don't get me wrong though! I'd been in a Zelda lull and this game did help me back into the series. It captivated me. I had half-days in high school and I'd race home to play it all afternoon and evening. I even lost a girlfriend to playing it too much, and frankly, I think this game saved me from a worse fate!
Metroid II: Return of Samus - Sure, it's the black sheep of the series, but it's the only game that I played over and over and over and over again in order to get a better and better time. I think my final one was something like 1:36. I have a photo of it somewhere... At any rate, this Metroid got me into the series, the first one just didn't do it for me until much later. I've very fond memories of a friend and I playing this game at the same time on two different systems for days on end, trying to out-do each other.
Star Wars: Rogue Squadron - I never cared for flight games, but I was a newly christened Star Wars fan and this game was the bees knees. It pushed the 64's graphics to the limits, and was highly replayable. I played it long after it was not considered current anymore. Great stuff.
Super Mario Bros 3 - It's sad that it's now available for $5 on the VC, since I did chores an entire summer to pay off the $99.99 price tag it was released for. So many levels, so many secrets, so many hours played. Everyone I knew owned this game, and we'd pop it in and play every chance we got.
Super Mario 64 - I think kids of today are spoiled. When this game came out, it was simply jaw dropping. Mario in 3-D was call your relatives, fake an illness to skip work, mind-blowing. I was too old for sleep-overs anymore, but upon playing this, my friends and I had one last sleepover to keep on playing. I don't think anyone slept though.
Super Mario RPG - The only real RPG I ever got into, mainly because of the Mario theme to it. But once I was past that attraction, I found a brilliant RPG laying in wait. I only ever rented this one, but I did so for a few weeks running until I beat it. Excellent gameplay, and highly addictive.
Super Metroid - Scared me stupid for some reason, but wow, what a game. The exploration, the animation, the music, the gameplay - it just all worked here. Great through and through, and probably, along with ALttP, the first game I played that truly felt epic in terms of story. What an ending!
Tetris - How can I not include it? It's the same damn game on every system with a bit of tweaking, yet I've bought it so many times. It's just addictive, and wonderful.
Honourable mentions that would probably rotate in and out depending on my mood -- Smash Bros Brawl, Donkey Kong Country, Mario Kart 64, Super Mario Bros, Legend of Zelda, LoZ: Twilight Princess, Spider-Man 2, Star Wars Knights of the Old Republic, Star Wars Battlefront II.