NES-
Ninja Gaiden 2 - I'm going to restrain myself from listing dozens of platformers, but this one is a true masterpiece of the genre.
The Legend of Zelda - obviously
River City Ransom - often considered the best game published for NES, or just behind Zelda 1. This was
Yakuza in 1989.
Crystalis - want a game that takes you on a fantastic journey? This is it.
Jackal - The reason that the NES comes with two controllers. Every element works in synch to deliver a perfect challenge for 2 players.
Genesis-
Shadowrun - Rockstar ought to cut Blue Sky Software a fat royalty check for the game that inspired them to make GTA.
Battletech - Vs all the armies of the Inner Sphere, my bid is... 1 lone Mad Cat. This is
Jackal, but with a Mad Cat.
Phantasy Star IV - The quintessential jrpg
Ecco the Dolphin - Beautiful and sui generis, with a real "sink or swim" difficulty.
Shinobi 3: Return of the Master - the other ninja platformer masterpiece
Steel Empire - Of all the shmups I've ever played, this one stands out for letting you choose between two very different vehicles, for the steampunk aesthetics, and for having levels of perfect length and difficulty.
Master of Monsters - This Genesis exclusive, which inspired Battle for Wesnoth, is a must for any tactics game afficianado.
MAME/ Arcade-
Not going to list the classics like Gauntlet and Street Fighter 2, ok?
Gain Ground - like a tactical shmup
Bomberman World
Dungeons and Dragons: Shadow Over Mystara
Boogie Wings
King of Fighters XIII - Still SNK's magnum opus
Neo Geo-
The Last Blade/ The Last Blade 2
Garou: Mark of the Wolves
Windjammers
The Super Spy
Crossed Swords
Gameboy/ DS-
Final Fantasy Legend 1 - If you thought FF8 was SquareSoft on crack...
Final Fantasy Legend 3
Link's Awakening
Yugioh World Championship 2008