Aside from the obvious (SMB3, Sonic 2/3/& Knuckles)...
Worms and Worms 2 (PC) Sheer manic genius.
Guardian Legend (NES) A space based shooter beautifully woven with a ground based shooter. A difficulty curve just barely out of reach. Compelling story to move it along, and a rare female main character, forgotten to the likes of Samus Aran.
8 Eyes (NES) Complete ripoff of Castlevania, but still fun in it's own right.
Bionic command (NES) Apparently good enough for a 3D revival later this year. So long as it holds up, I'll be happy.
Battletoads (NES) Okay, so I think we can all admit to hating that damn underground racing sequence, but the rest of it was good, right?
Willow (NES) Horrible movie, bad music for the first two towns, quasi-Zelda ripoff, but if you can figure out even how to get into Bavmorda's castle, you win.
Rampart (NES) Simple premise, impossible to master.
Nintendo World Cup Soccer (NES) If you know what you're doing, it is entirely possible to end a game 96 to nothing. Try THAT in real soccer (or football, wherever you hail from)
Ninja Gaiden 1-3 (NES) Also apparently good enough for a 3D revival. I haven't tried the new ones myself, but I've heard good things.
Startropics 1 & 2 (NES) Apparently forgotten by Nintendo in recent years as they haven't tried milking the franchise to death, but with such an awesomely out there story line, maybe that's for the best.
Vectorman (Genesis) I may not get the first person shooter genre, but the side scroller genre I do get, and this is one of the greats.
Earthworm Jim (Genesis) Faithful in every respect to the cartoon which spawned it, and that's a very good thing.
SimCity 2000 (PC) What can I say? Hell yes, I still play it. Far more than I ever play SimCity 3000 or 4.
SimTower (PC) WHY? Why do my tenets keep leaving my nice buildings? What more do they want from me?
SimIsle (PC) My PC hated me for trying to run it. And somehow I always ended up building stuff too close together so they couldn't expand when necessary. I just wish my install disk weren't so far gone...
Where in the USA is Carmen Sandiego? (PC) Sure, it's a point and click kind of deal, and it's educational, but you're catching criminals too!
And finally Spiderman for the XT Gold operating system on an computer manufactured by AT&T some time during the 1970s. Weird as all hell, impossible to find any information on now, but superb in every way.
There may be more, but I hope not...
[EDIT] I knew it: someone had to go ahead and remind me Atari existed, which brings me to:
Kaboom. Impossible. Simply impossible. And yet, still good times.
Warlords. Kind of like Rampart, except there's only one cannon, everyone uses it, and you don't rebuild your walls.
And, for the Atari 7800: Food fight. Nothing more needs to be said.
I don't mention SNES because I didn't have one until the system was long past dead, but what the hell, Donkey Kong Country deserves mention here too.
[SECOND EDIT] Gah! Gameboy! Of course! Super Mario Land, Revenge of the Gator, Donkey Kong (1994) and... the immortal Tetris. I apoligize for forgetting Gameboy (but not for the incredibly long post now made even longer.)
[THIRD EDIT] And I still forgot Oregon Trail! I'd always die, but my family would make it, those hardy pioneering souls.