I'm pretty sure there's an entire website for exactly this subject, but I'll add myself to this thread anyway.
50. Yo Yo's Puzzle Park (Irem, 1999) This game oozes charm at every turn. It's a bit fiddly to get used to, but it ceartainly plays well, even if it's more action than puzzle.
49. Mega Man (Capcom, 1987) Who needs reasonable challenge curves when you can take enemy attacks and make the next boss a cakewalk? It's cheating, but fairly. I'd have liked better menu layouts, though.
48. Super Smash Bros. (Hal Laboratory, 1999) The game that got me properly into video games, I just had to put it on the list. This game introduced to me not just the concept of button mashing, but so many faces that have stayed with me over the last decade, some of whom I've still never seen on their own.
47. Super Mario World (Nintendo, 1990) Such a massive, time consuming game. Few releases can claim to have this much in terms of scope, on top of the trademark excellent gameplay design. I didn't put it higher because I find it to be too big for it's own good.
46. Sonic Adventure 2 (Sega, 2001) Arguably the only time Shadow was ever used well as a character, this certainly had a more immediate feel than the first game but gives one slightly less freedom. The levels had a good flow to them and the mini-games were fun.
45. Wario Ware inc: Mega Party Games (Nintendo, 2003) There's a minigame about picking your nose.
44. Pikmin (Nintendo, 2001) While the time restricion is something completely unnecessary, this game has so much charm that you can't help but smile at it. Not to mention the fact that the level design is really good.
43. Crazy Taxi (Hitmaker, 1999) Oh, the hours I've spent just mucking about in this game. There are few things more enjoyable than when someone still praises your driving skill even after you drive like a maniac.
42. Kirby's Dream Land (Hal Laboratory, 1992) Certainly not the hardest game in the world, but somehow I still get a sense of achievement and inherient joy every time I complete this.
41. Super Mario Bros. 3 (Nintendo, 1988) I honestly didn't know Devid was going to put this game in the exact same spot as me, but oh well. While this third installment certainly had a number of the same problems as it's successor, there's a much better sense that you're being driven foward. In fact, Super Mario Bros. 3 seems to have much more variety in it's level design and environments than much of Nintendo's later offerings. Also, the power-ups control better in this one.
40. Micro Machines V3 (Codemasters, 1997) Do I need to elaborate on the enjoyment from leaping off milk cartons into bowls of cereal? If only I could still find my copy.
39. Super Smash Bros. Melee (Hal Laboratory, 2001) This series is one of the few fighting games where the environments are characters in themselves. I'm sure there are things I still haven't unlocked.
38. F-Zero X (Nintendo, 1998) I know, it's certainly not the prettiest game of it's era, even the blocky environments of SM64 look better, but that means it runs so smooth and the sense of speed is so great.
37. Crash Bandicoot (Naughty Dog, 1996) Even with D-pad controls this packs so much punch. You can never beat a story about a crazy scientist working on animals, can you?
36. Pac-Man (Namco, 1980) There's a poetic charm in this game's simplicity. Eat, run, eat eat.
35. New Super Mario Bros. (Nintendo, 2006) The game that made 2D platforming the new black, this entry was so good with it's secrets and it's proper pacing that few other entries have got right.
34. Sonic Advance (Sega, 2001) One of the best mixes of speed thrills and solid platforming around.
33. Starfox 64 (Nintendo, 1997) A proper interactive movie experience. I'll never get that rabbit's commands out of my head.
32. Spyro the Dragon (Insomniac, 1998) A great mix and furious fire-breathing action and semi-solid platforming. There's a bit of a depth-perception issue that isn't in other games, but not too much.
31. Kurushi Final: Mental Blocks (Sugar and Rockets, 1998) This is probably one of the easiest sorts of game to make a level editor for. Come to think of it, so is any game with grid-based levels. Don't ask me what the point of the IQ score is.
30. New Super Mario Bros. Wii (Nintendo, 2009) At last, they managed to get the sense of scale just right. The boss fights are their usual easy selves, mind.
29. Kirby and the Amazing Mirror (Flagship, 2004) A properly shining example of exploration platforming done right. The whole dopple-ganger thing got a bit confusing.
28. Legend of Zelda: Four Swords Adventures (Nintendo, 2004) This certainly felt more like an old-school arcade beat-em-up mixed with a dungeon crawler than anything else that has ever been called Legend of Zelda, but it's frantic and over-the-top and the co-op mode works well, for the most part.
27. Super Smash Bros. Brawl (Hal Laboratory, 2008) I never understood why they included Solid Snake, the exact opposite of a Nintendo character, in the roster. Sonic, yes, but Solid Snake hasn't been in an E-rated game at all, I don't think.
26. Mario Kart Wii (Nintendo, 2008) Another party game from the same people in a row, I know I'm not throwing many surprises your way. Definitely the Wii game I've spent the most time in multiplayer, the remote was made for this type of game. Now if only I could get to grips with manual gear.
25. Sonic the Hedgehog 2 (Sega, 1992) The only one of the classic trilogy to get everything right. A perfect balance of speed and platforming that doesn't get dull.
24. Rayman (Ubisoft, 1995) There are few things that can beat punching a guy from behind while standing in front of him.
23. Kirby's Adventure (Hal Laboratory, 1993) Rarely can a game pull off making you kick yourself over a secret you know is there but just can't work out how to get to. They need to be designed like that more often.
22. Donkey Kong Country (Rare, 1994) This game flows so well. Mastering this is a beast.
21. Pikmin 2 (Nintendo, 2004) All the charm of the first game, but now you aren't forced to complete it in a certain time like you're clocking off for work early. Really a game you can lose yourself in.
20. Sonic Adventure (Sega, 1998) The open-ended structure of this solid platformer make exploring this world such a joy. If only these guys did the voice acting in the newer ones.
19. Mario Kart 64 (Nintendo, 1996) Pretty much the only Mario Kart game to get both the party and the driving skill in one complete packages, and this version of Rainbow Road was definitely the best.
18. Crash Bandicoot 2: Cortex Strikes Back (Naughty Dog, 1997) Though I never got far into this second game, I certainly found the levels to be a lot smoother. The use of power-ups improved the formula a good deal.
17. Super Mario Bros. (Nintendo, 1985) Everything about this game is just pure joy. Who'd have thought that basing a jumping mechanic around the laws of momentum with make for such a compulsive game? Even with the warp zones and the minus worlds we all know of, I wouldn't be too surprised if someone tries to show us all another secret.
16. The Legend of Zelda (Nintendo, 1986) Just running in any direction. That's what freedom is. It doesn't matter what order you do the dungeons in, just do them in your own time. Open world gaming at it's most basic level, but one of the most engaging open world experiences you can find. Don't spend ages looking to the device that drives the plot forward, just explore.
15. Super Mario Galaxy (Nintendo, 2007) If any game deserves to be called incredible, this is it. Gravity physics made this already solid formula so much more engaging. Though, if I'm honest, I was kind of let down by it. For a series whose 3D installments pride themselves on exploration, the levels felt dissapointingly short and linear, and just getting to them was a bit of a pain in the neck. And the barebones attempt at storytelling was a step backward after Sunshine's above-average efforts.
14. Paper Mario: The Thousand Year Door (Intelligent Systems, 2004) Few times have over-the-top charm have been this mechanically solid in a turn-based RPG, but this pulls it off, even if Mario is the only character who levels up in a way that doesn't feel completely arbituary. The plot is full of laughs and the out-of-battle mechanics have some thought behind them.
13. Professor Layton and the Curious Village (Level 5, 2007) I'm still wrangling over the puzzle in the clock tower to this day, and normally I forget about small things like those pretty quickly. That's what this game does. It makes you think about things deeper than you would otherwise.
12. Kula World (Game Design Sweeden, 1998) I'll hold this up as the game that best represents the original Playstation and what it was about. It wasn't made great by a face or name on the cover, it was great because it was bright and colourful, and had an awesome techno soundtrack, and played so smooth, and really sent your thoughts into overdrive, and it had an incredible sense of style. The PS1 wasn't about the big games, it was all about the weird ones. Where else would you find a beach ball collecting sunglasses 10,000 feet in the air?