I'm not sure if I'm happy with my list - the numbering after the top 10 especially got iffy. But... I gave it my best, I suppose.
1. Super Mario Bros 3 (NES)
The undisputed king in my eyes. Perfect level design, sense of challenge, complemented with rewarding exploration with secrets and an unusually fun versus multiplayer.
2. Final Fantasy IX (PSX)
Charming throughout, the story is the rare kind that actually engaged me and made me care for each and every one of the characters. The gameplay was immensely satisfying and Chocobo Hot & Cold is more or less the greatest idea ever.
3. The Legend of Zelda: Ocarina of Time (N64)
While I find myself enjoying Wind Waker more, whenever I think of a great game, this instantly pops into my head. I'll never forget standing in front of the demo at Target and just watching this insane world reveal itself before me, and every moment of this game is absolute perfection.
4. Demon's Souls (PS3)
Challenging and rewarding, moreso than any other game I can think of because it's constantly so fair. Your every encounter is a test of your nerve, not to mention when you contest dragons and demons.
5. Jak II (PS2)
Platforming joy and humor place this here for me. I had a hard time deciding which Jak game to place here, but in the end, Jak II has my favorite platforming challenges, and the variety of gunplay and racing really nails the dynamic.
6. Mirror's Edge (PS3)
Platforming bliss with beautiful visuals. It rewards creative thinking and pushes you to your limits.
7. Disaster: Day of Crisis (Wii)
Arcade-styled fun with a mixture of gunplay and motion-controlled life-saving. The soundtrack is immense, and the story is almost too silly.
8. Valkyrie Profile 2 (PS2)
The most satisfying RPG battle system I find myself likely to ever enjoy, unless Resonance of Fate topples it. Moreso, unlike most others opinion on the matter, the latter half of the story is when I finally begin to really enjoy it, as it blasts you with ridiculous notions of time-travel, deceit, and crazy shit. Awesome.
9. LocoRoco 2 (PSP)
My favorite PSP franchise had to place on here in some form. While I'm greatly enjoying Midnight Carnival at the moment, and love it's heavier emphasis on platforming, the original hide'n'seek mechanics peaked here in LocoRoco 2. The beautiful music and amazing presentation really helped a great deal, as well.
10. Bubble Bobble (NES)
The hours I've spent playing this with family and friends are uncountable, but I wouldn't trade them for the world.
Runners-up
11. Final Fantasy VII (PSX)
The first game I ever played that essentially defined my transition into gaming as a serious hobby, and a serious part of my life. The pre-rendered backgrounds set the atmosphere perfectly, the music was stunning, and yes, I even like the story, even to this day.
12. The Legend of Zelda: Wind Waker (GCN)
While the visuals may define it, I still love every moment of the gameplay; it would be years, and several playthroughs, before I found out people complained about the triforce fetch quest, as I loved every moment of the game, from the sailing to the initial stealth dungeon.
13. Odin Sphere (PS2)
Lush visuals with tactically challenging gameplay that forces you to take note of your inventory and reflexes. The story is incredible, the music is incredible, the voice acting is incredible... when all is said and done, the only reason this didn't make the top 10 is because I didn't like playing as the girl with the crossbow.
14. Valkyria Chronicles (PS3)
Supremely enjoyable combat, and excellent presentation. When I finished the game, I didn't even pause for a moment; I jumped into the new game+ immediately. Demon's Souls is the only other game on this list I've done such a thing with.
15. Super Mario Galaxy (Wii)
I didn't like the water levels, okay? Otherwise it'd be higher, because every other moment is pure joy and happiness.
16. Final Fantasy Tactics: War of the Lions (PSP)
I much prefer the new translation, and the various downsides of the port did not bother me in the least. The new FMVs are stunning, and I love the voice-acting (who would have thought Phil LaMarr to be the perfect Ramza?). The gameplay is uniquely challenging as it forces you to use the limited abilities it gives you, rather than loading special attack upon special attack upon you.
17. Sonic and the Secret Rings (Wii)
Initially I had Sonic the Hedgehog in this position... but the more I thought about it, the more I realized SatSR was my favorite platformer in the series. It was fun, and the constantly-running mechanic really brought a unique platforming feel to the genre.
18. Front Mission 3 (PSX)
Huge on content and customization, and an absolute thrill from start to finish.
19. Ico (PS2)
Beautiful, haunting, and immersive. The puzzles are fantastic, but unfortunately the shadow-enemies bring this game down a notch.
20. Mickey & Donald in World of Illusion (GEN)
Co-op gaming with childhood heroes, travelling through what I still consider some fantastic environments. I love the sound, I love the music, I love everything about this game.
21. Super Monkey Ball (GCN)
In typical Sega fashion they couldn't get it right beyond the first time. The original Super Monkey Ball has the best level design in the series, with incredible challenges that test your skill as opposed to your luck, and the mini-games are still without a doubt the best to be had.
22. Champions of Norrath (PS2)
Enter here: the whole genre of console co-op dungeon crawling. Collecting loot as you crawl through monster-filled caves and cliffs with a friend beside you is my idea of heaven.
23. Discworld Noir (PC)
The humor felt as genuine as one of the books to me, and the over-the-top noir scenarios simply made it all the better.
24. Grim Fandango (PC)
Needs no introduction or even explanation, I would imagine. Simple an excellent fucking game.
25. Infinite Undiscovery (360)
Yes, I'm serious. I found the gameplay to be an absolute joy, and even really enjoyed the story as I found Capell to be positively hilarious. It's a shame this series will certainly never see another installment, but I hope some of the ideas eventually make their way into other games.