I'd play these everyday, even when I had friends come over. Fun times.

Mortal Kombat I and II
Street Fighter II
Contra
Donkey Kong Country
Streets of Rage
Punch-Out!!
Killer Instinct

and several others...

It may not be one of the best, but it is one of my favorites: Batman Returns.

Anything before the 16-bit era.

My two favorites are Killer Instinct and DKC 2.

To me

Saturn: Fighting games.
NES and Genesis: Platformers/action adventure, etc...

Coming up with just one console it's almost impossible, since so many great games are spread all over different systems.

But overall: I think the Genesis, SNES and PS2 have pretty much almost everything one needs.

Street Fighter Zero (Alpha) 3: The reason why I got a Saturn, Arcade Perfect. My favorite game in the whole series too.
Guardian Heroes: Probably the best Beat Em-Up I've played, really fun specially when you have more people to play with.
NiGHTS... Into Dreams: Saturn didn't have Sonic... But it had this gem, and it is one of my top favorite games.

Get it, it has 3 of the best Mega Man games in one but with better visuals… (not so much on the sound department though, I prefer 8-bit music) still it's the same game play and very fun to play. If you have a PS2, GC or XBOX get the Anniversary Collection, you get Mega Man 1-8 in one disc plus 2 fighting games. Be sure to check out the Mega Man X series as well.

Add these to the list:

Castlevania: Bloodlines
Contra: Hard Corps
Revenge of Shinobi
Thunder Force III and IV
Vectorman 1 and 2
Rocket Knight Adventures
Splatterhouse 3

Batman Returns
Spider-Man & Venom: Separation Anxiety
Captain Commando
Ninja Warriors

The SNES version was the toughest in my opinion, the enemies seemed to fight back a bit more than the other versions of the game. The NES and Genesis versions were similar in difficulty at least from what I've played. Whichever version it was, this game was awesome and still is quite enjoyable.