Nice topic Heather, here's the list:
1. The Beatles: Rock Band (PS3) - despite I'm a platformer fanboy, this is surely my favourite game, since it's actually the only game that did something good to my life (not just "wasted time", as some people would say) - it taught me how to play drums
Sorry, but you just won't learn how to use a gun from Ratchet & Clank.
2. Ratchet & Clank: Quest for Booty (PS3) - Yeah, in the first place I'm placing the games that somehow affected my life, and QFB is one of them. Despite it's my first platformer and without it I would never play over a half of games from this list, it's just got the greatest balance between platforming and shooting. It also brought us new Omniwrench, wich found a lot of good uses, also in ACiT.
3. Ratchet & Clank: A Crack in Time (PS3) - it was a hard choice beetwen this and ToD, but when I compared plots of both games, ACiT just won.
4. Ratchet & Clank: Tools of Destruction (PS3) - the best Ratchet since the forst on. Platforming strikes back.
5. LocoRoco (PSP) - There are three games that I bought music from. R&C: A4O, Sly 4 and LocoRoco. And the last one wasn't so cheap as the others (really). Since music, charm and really inventiv gameplay mechanics make LocoRoco something unique - a game, that everyone (in every age) will enjoy.
6. Sonic Generations (PS3) - as much as bad the plot is, Sonic Generations is a blast… that allows you to blast through awesome levels. Speedrunnig is just something cool.
7. Jak 2: Regenerade (PS2) - The most mature and the hardest series I've ever played. I really respect Naughty Dog not only for a game itself, but for an incredible graphical achievement (back then) Despite Jak 3 is "better", I like Jak 2 more. It's just Jak's desing and more of Haven City.
Jak & Daxter: The Precursor Legacy (PS2) - more kiddish and platforming than the next ones, but sure great.
9. Jak 3 (PS2) - didn't I just write about it? 
10. Sonic 3 & Knuckles (complication) (Mega Drive) - Sonic one was OK, Sonic 2 wasn't for me… but Sonic 3 & Knuckles (2 games in 1) just made me think "How was this even possible back then?" It's just sad to know it was the last good Sonic game until 2010.
11. Ratchet & Clank: Full Frontal Assault/Q-Force (PS3) - I really hate the campaing and fact that Insomniacs actually made this game, but finally I can test my skills in a solid (and working…
multiplayer.
12. Sly 2: Band of Thieves (PS2) - Finally. While making this ranking, I didn't realize Sly will be in those "less lovable" part. Sly 2 actually made Sly modern. While Sly Racoon was an oldschool platformer, continuation of Crash Bandicoot (at least I heard so
), it's sequel brought more complicated and interesting mechanics. And of course it knocked out Ratchet and Jak in "the best music" category (sorry David Bergeaud fans).
13. Ratchet & Clank (PS2) - Big congratulations for doing such a big game (and franchise) Insomniac.
14. Sly Cooper: Thieves in Time (PS3) - Sure Sanzaru didn't make a revolution in the series (it's mostly what we've seen on PS2, just on the next-gen, but it's actually more fun than Sly 3 and… seriously, Sanzaru was the only studio that actually thought about making next Sly. If not them, there would probably not be any Sly anymore.
15. Age of Empires III (PC) - Five years ago I was making colonies in the New World (America) and fighting for them as a real historical nations. I understand my dad's flustration, when he see's me playing all the other games mentioned here (with the exception of the number one).
16. Sly Racoon (PS2) - What can I say, a fun platformer.
17. Sam & Max (new series) (PC) - If you played these games, you know you shouldn't mess with the freelance police. It's dangerous…
18. Toy Story 2 (PC/PS1) - Even before becoming famous because of LEGO games, TT made a great (but somehow) forgoten platformer. To infinity, and beyond!
19. LittleBIGPlanet 2 (PS3) - I'm not a great creator (at leats not yet) but I can sense the editor's infinite power.
20. LEGO Batman (PC/PSP) - another childhood memory, my favourite LEGO game.