NES:
Layla (import only, but that's no excuse)
Bionic Commando (beats the arcade version BY FAR)
Strider (almost as good as the arcade game, but still underrated)
Terranigma (IMO better than A Link to the Past)
Section Z (beats the crap out of the arcade game)

SNES:
Uniracers (lots of fun)
Pop 'n Twinbee: Rainbow Bell Adventures (great Twinbee game =) )
Shonen Ninja Sasuke (great Sunsoft title)

Genesis:
Comix Zone (lots of fun, great moves and dialogue)
Kid Chameleon (a dude that can transform into pretty much anything? Great!)
Shinobi III (a lot of people I know hate it but it's awesome)

PS1:
Mega Man Legends (IMO the greatest MM series there is)
Misadventures of Tron Bonne (quite fun)
Saga Frontiers 1 and 2 (I don't care what anyone says )
Point Blank (great party game)
Ore no Ryorui/I'm the Chef (great import cooking game)
PaRappa the Rapper
Um Jammer Lammy (still the best two music games yet)
Tomba! 1 and 2 (great platformers)
Breath of Fire IV (some people like III but not IV too much it seems)
Gokujyou Parodius! (fun, fun, FUN!)
Thunder Force V

Other games:

Crisis Beat
Dynamite Cop
Lufia 2
Rakuga Kids
Project Justice
Mega Man Battle & Chase
Soukyu Gurentai/Terra Diver (awesome!)
Trap Gunner
Battle Circuit