Here's my list, in no particular order:
1) Star Wars: Knights of the Old Republic (Xbox / PC)
My favorite RPG ever. The storyline was epic, and way better than the most recent 3 movies, IMO. The combat system was a little clunky at first, and some of the exploration was pretty linear, but once you got the hang of how everything worked, the gameplay was great, and looked incredibly cinematic. Basically, if you haven't played this game, go get it and play it.
2) Halo 1 (Xbox)
I used to be pretty big into FPS games, and the reason was probably a combination of Halo and the first game of my honorable mentions section. Halo was epic, with huge outdoor environments, kickass vehicles, and amazing gameplay. One of my favorite moments in all of gaming is coming across a field of snow in the mountains with Humans fighting covenant all over the place, fighting my way through the battlefield and stealing a banshee to make my daring escape. Besides the awesome single player campiagn, some of the best times I've ever had have been LAN parties playing this game. I remember sitting in the basement of a freind's place, with a bunch of TVs and Xboxes set up, with 16 of us killing each other over and over. My freshmen year of college, I didn't do homework I played Halo.
3) The Elder Scrolls III: Morrowind (Xbox / PC)
When I first played this RPG, I played for about an hour and was like, "This sucks. I don't really even know what I'm supposed to do." So I stopped playing. Awhile later, I started playing it again, with a different mindset. I think when I first started playing it, I was just overwhelmed. I was used to playing games where if there was an item on the ground, you picked it up because it was going to be useful to you. In Morrowind, if you picked everything up, you'd get busted for stealing and have to pay a fine or go to jail. Once I started picturing Morrowind as a virtual world, it started to make a whole lot more sense to me. It's completely non-linear and the world is just massive. The experience was like being a real adventurer, making a long journey out into the middle of nowhere to accomplish quests, finding random dungeons to explore, etc. Oblivion, the next game in the series, was an excellent game as well, but IMO, Morrowind was the better game.
4) The Legend of Zelda: Ocarina of Time (Nintendo 64)
I've never played a bad Zelda game, but this one is by far the best, I think. Making the transition between 2D and 3D would be a pretty difficult task, I would think, but Nintendo pulled it off beautifully. I won't go into too much detail on this one, because Zelda is Zelda, and if you haven't played a Zelda game, you're not a real gamer.
5) Half Life 2: The Orange Box (PC)
Okay, I might be cheating on my own rules here about only 1 game from each franchise, since The Orange Box has 5 games in it, but this is some of the best money I ever spent on a video game. It was like 30 bucks for this, and I got so much enjoyment out of it that it felt like I should have paid a lot more. I'd call it a FPS, but it's really so much more than that. I've played through Portal about 5 times, and I'm working on playing through HL2 and Episodes 1-2 again. My most memorable moment in the game: Stepping on the sand would cause bugs to come up from the ground and maul you, so you needed to use the gravity gun to pick up random debris strewn around the beach to make a bridge from rock to rock. It's like the mature version of Lava Tag. Anyway, this is well worth picking up, if you haven't.
Honorable Mentions:
Goldeneye (N64): paved the way for modern FPS games, especially in multiplayer. I played this game a frickton.
Beyond Good and Evil (Xbox): An incredibly underrated Action/Adventure game. Think of it like a Sci-Fi Zelda game with a sweet storyline.
Kingdom Under Fire (Xbox): A really unique game. Kind of a cross between a RTS and a hack and slash game, you took command of troops on a battlefield. You felt like a commander in a midievel war, and the gameplay was really quite deep. Simple things like making sure your archers didn't have the sun in their eyes or hiding your troops in a forest to avoid arrows made it really immersive. Best memory of this game: Playing a multiplayer game with a friend of mine. He had only a few infantry left, I had 3 archers and some aerial dragons. He hid his infantry in the trees to avoid my arrows and dragons, so I had my archers set their arrows on fire and set the forest ablaze, forcing his troops out to where my dragons could finish them off. Epic.
I'm sure there's other games I'm forgetting, so maybe I'll edit this later. Until then, anyone else? I went a bit more into detail than I thought I would so feel free to make yours shorter :)