NES:
Final Fantasy I - III
Contra
Bubble Bobble
Megaman I - VI
Double Dragon
Super Mario Bros I - III (optionally skip II)
Bionic Commando
Deja Vu
CastleVania
CastleVania III
Legend of Zelda
DuckTales
Metroid
SNES:
Chrono Trigger
Final Fantasy IV - VI
EarthBound
Secret of Mana
Super Street Fighter II
Contra III
Starfox
Zelda: A Link to the Past
Lufia II
Shadowrun
Super Mario World
Super Metroid
N64:
Super Mario 64
Goldeneye
Conker's Bad Fur Day
Perfect Dark
Zelda: Ocarina of Time
Zelda: Majora's Mask
PS1:
Rayman
Crash Bandicoot I - III
Final Fantasy VII (i liked it
)
Final Fantasy IX
Resident Evil I - III
Spyro (I forgot which ones are good, just skip the first one and it'll probably be fine)
Tomb Raider I - III (although you should probably play the PC versions instead since they have unlimited saves rather than gay save crystal bullshit)
Mortal Kombat III
Dino Crisis
Heart of Darkness
MediEvil
Metal Gear Solid
Dreamcast:
Dead or Alive II
Chu-Chu Rocket (my dreamcast came packaged with this
)
Crazy Taxi
D2
Soul Calibur
Daytona USA
Shenmue I and II