My short mandatory list:

NES:
Super mario bros 1, 2 & 3
Zelda 1
Batman 1
MegaMan 2
Little Nemo The Dream Master

SNES:
Super Mario World
Yoshi's island
Zelda 3
Donkey Kong Country 1 & 2 (don't bother with the third)
Street Fighter 2 turbo (any version with turbo in it)
Another World / Out of this World (US name). This one exists on PC and other platforms.
Super Mario Kart

N64:
Mario 64
Zelda OOT
GoldenEye 007 & Perfect Dark
Banjo-Kazooie & tooie
Mario Kart 64

PS1
Metal Gear Solid
Castlevania Symphony of the Night

It is not a lot but all of these games are really amazing ones, even by today's standards.

River City Rampage (NES) still holds up pretty well. Super Metroid and Street Fighter II are my favourite of the pre dreamcast games though.

The Legend of the Mystical Ninja