Edit- I forgot Paper Mario: TTYD. And Crash Team Racing. Whoops.
Anyway, I had trouble narrowing it down to 20, so ended up doing a top 20 followed by a top 20 honorable mentions:
In alphabetical order by format:
Mass Effect 2 360 Fixed a lot of faults with the original and is far better as a result
Ouendan 2 DS Easily my most played DS game, spent ages trying to get the best ratings on the highest difficulties
Phoenix Wright: Trials and Tribulations DS The perfect end to an incredible trilogy
Pokemon Fire Red (or Yellow) GBA Yellow for pure nostalgia, and having Pikachu following you, but Fire Red was objectively better.
Fire Emblem GBA/Wii U My favourite Nintendo franchise. The sprites in the GBA games have the most charm, they're lovely.
Super Mario Sunshine GC/Wii It's not the best Mario game but it's my favourite. We spent just as long exploring the world as playing it properly.
Sonic the Hedgehog MS Nostalgia plays it's part, but it still looks lovely and plays brillianly.
The Curse of Monkey Island PC Comfortably my favourite point and clicker, including perfect voice-acting, a fantastic art style and fiendish puzzles.
Spyro 3: Year of the Dragon PS1 The best Spyro, and the best platformer on the PS1. Superb stuff.
Jak and Daxter: The Precursor Legacy PS2/3 Only game I have finished three times and it holds up incredibly well.
Portal PS3/PC The first FPS I properly enjoyed, it was amazing
Donkey Kong Country 3 SNES Nostalgia strikes again: loads of memories playing this in co-op.
SMW2: Yoshi's Island SNES First game I finished
Sunset Riders SNES Amazing co-op western-themed 2D shooter
Super Mario World SNES My first game
Zelda: A Link to the Past SNES First Zelda. Had no idea what I was doing, but explored it so much.
Zero Escape: Virtue's Last Reward Vita The most confusing, mind-boggling and gripping game on the Vita. Such a shame there's no sign of the sequel being made.
Mario Kart 8 Wii U Doesn't have the nostalgia factor like CTR but the best kart racer ever made
Rayman Legends Wii U Secret best 2D platformer of the decade
Sonic Racing Transformed Wii U Best career mode of any kart racer, playing everything in co-op was brilliant. Wii U best due to the use of the gamepad
Honorable mentions Assassin's Creed 2 360 Introduced Ezio, the best character in AC, and finally delivered on what the original promised.
Geometry Wars 2 360 The best 360 game. Fact.
GRID 360 Best non-kart racing game
Kinect Sports Ultimate 360 The game of choice when families come round at Christmas. Bowling and golf are particular highlights.
Ghost Trick DS Another great Shu Takumi game, just as good as Ace Attorney
Advance Wars GBA Lacks the heart of Fire Emblem, but incredibly addictive
Castlevania: Aria of Sorrow GBA My first Castlevania game, and it was a blinder. Outstanding music, too.
Fire Emblem: Sacred Stones GC Pretty much interchangeable with Fire Emblem in my actual top 20
Chibi-Robo GC This was a huge surprise, ranks alongside Pikmin as the best new IP on the cube.
Tales of Symphonia GC One of my first RPGs, and it was an epic one. Heard it hasn't aged well, so I'd rather not play the remake.
Pac Man CE DX PC Incredibly addictive and took the place of Geometry Wars 2 when I unplugged the 360
Final Fantasy X PS2/3 My first PS2 game and my first Final Fantasy.
Portal 2 PS3 Will probably replace Portal when I get around to playing the co-op campaign. Main game was superb.
Tomb Raider Reboot PS3 Better than Uncharted, fantastic game
Uncharted 2 PS3 The best of the Uncharted Trilogy. Looks superb, great sense of humour and decent shooting action. XCOM: Enemy Unknown PS3 Doesn't run well on the PS3, but superb strategy, looks good and is incredibly addictive
The Last of Us (Remastered) PS3/4 Superb atmosphere, lovely characters and brutal gameplay, just as good to watch as to play.
Super Bomberman 2 SNES Hectic multiplayer action, and a good SP campaign to boot.
Super Mario Galaxy 1 & 2 Wii Will probably force their way into my list when I replay them
Pikmin 3 Wii U The pinnacle of Pikmin, and might make the top 20 after I play the mission mode
Crash Team Racing- Can't believe I forgot this.