1) Chrono Trigger (SNES):
Lotsa people complained about the difficulty level and length - but I think those two aspects can be pulled off in many-a-game. It's strength is its characters and storyline, two aspects where many games these days, fail.
2) The Legend of Zelda: a Link to the Past (SNES):
Classic Zelda game that, I think, really got the series moving. I mean, the orginal
LoZ had the overworld and didn't lead players by the nose, which was brilliant considering gaming back then. But the storyline and gameplay took a huge leap with this classic <3.
3) Paper Mario: The Thousand Year Door (GCN):
Some of the best dialogue I've ever come across in a game. Absolutely hilarious. A fun battle system that didn't get repetitive. Wonderful storyline. Lovable characters.
4) Sonic the Hedgehog 2 (Sega Megadrive):
I
love the music in this game. I never get sick of it. Vibrant colours, awesome stages, Super Sonic = awesome, and the classic LOL @ Dr. Robotnik being able to outrun Sonic on Death Egg, after Mecha Sonic and before you fight him in the last battle XD.
5) The Legend of Zelda: Ocarina of Time (N64):
Innovative, intricate storyline, gorgeous scenery, beautiful music.
The rest, I'll just list ^^:
6) GoldenEye (N64)
7) Super Metroid (SNES)
8) Super Mario World (SNES)
9) Streets of Rage 2 (Sega Megadrive)
10) Disgaea (PS2)
11) FFIV (SNES)
12) The Legend of Zelda: Link's Awakening
13) Donkey Kong Country (SNES)
14) Alex Kidd in Miracle World (Sega Mastersystem)
15) The Legend of Zelda: Adventure of Link (NES)
Edit: whoops, put SoR2 in the wrong console!