Wait, how the hell can people like Kane and Lynch 2???
My five favorite:
Legend of Zelda: Link's Awakening / Majora's Mask / Wind Waker (can't really pick between the three a definite favorite; they're all so perfect)
These for me are pretty much the definitively fun Zelda adventures. LA has the best classic Zelda experience, Majora's Mask has the best implementation of story, dungeons, and sidequests, and WW has the purest and most-fun sense of exploration and high-adventure in the series.
Super Metroid / Metroid Prime
The one game I think is essentially, and aesthetically perfect in every way. Prime is close, and pretty much essentially perfect as well, but both games are timeless and never get old.
Another game that does not stop being fun, ever. Squaresoft perfected the turn-based RPG with Chrono Trigger, and made a fun, unique, and engaging world to play around in. Mitsuda's score also borders on perfection.
This is probably Miyamoto's best game and masterpiece; everything about it is tight, fun, inventive, colorful, and bursting with charm. The game hardly ever goes below "incredibly fun", and everything from the bosses, the levels, and psychedelic Get Fuzzies are a treat.
Super Mario World
The other great in the list of greats. There is, as well, nothing wrong with this game, and is so chock-full of secrets and fun that it has kept me coming back to it time and time again.
Advanced Wars 2
Mega Man 2
Mega Man X
Metroid Prime 2 Echoes
Final Fantasy V Advanced
Super Smash Bros. Melee
Street Fighter Alpha 2
Super Mario All-Stars
Secret of Mana
Surprisingly, the majority of games i've listed come from the 16-bit era.