For me, personally, these are my favorites:
-Conker's Bad Fur Day. Probably the videogame I've played the most hours in my life, wish it had a counter. Multiplayer with friends was a blast we'd often have, but I was on it all the damn time, replaying the story mode but mostly playing against AI bots on multiplayer. Wish more current games had multiplayer AI bots.
-Perfect Dark. Pretty much the same as Conker, but I played it much less (still probably several hundred hours throughout so many years), it's still very dear to me and I still play the Xbox 360 HD remake relatively often.
-Majora's Mask. I was the only kid I knew who never owned Ocarina of Time (though I borrowed and beat it a few times), so it was Majora's Mask for me. It actually took me several years to beat, but every time I went through a timeline was an absolute delight. Timeless games, those two Zeldas.
-Paper Mario. I must've gone through this game a couple dozen times. Never tired of it. An excellent RPG, so sadly overlooked by many people. It's an absolute classic in my eyes, and I'm very glad it's on the Wii U's eShop nowadays.
-StarFox 64. Never owned it, but I would borrow it as much as friends would lend it to me. I loved that game, beat it going through all possible paths so many times! No other flight-sim has ever come close for me.
-Battletanx: Global Assault. My other multiplayer go-to game. Several hundred hours through several years, it provided many evenings' entertainment for me and my friends. It's a real shame there's nothing like it anymore. I'm fairly sure if it were to enjoy an HD remake, a ton of people would see it for what it is and go out and buy it.