Hmm... I'm going to mention a lot of games that would go without mention, if they didn't demand mention. So many to get through I'll probably have to post again.
For the SNES, there were the last great SquareSoft games. Final Fantasy 6 was operatic in a way none since have managed to match. It was just all around fantastic for it's time. Surpassed only by Chrono Trigger, which can only be called the best RPG ever. Bar none. Don't even think about it. And to be honest, I don't even really know why, so I can't even defend that. Oh yeah, and the Super Mario RPG, which was just loads of fun. They also made a platform-shooter-RPG called Front Mission: Gun Hazard, but it was never released outside Japan. You need an emulator and a patch for it.
Other games to remember were things like Harvest Moon, which was just irresistible; Battletoads, Earthworm Jim, and such, great time wasters from the heyday of platformers; plenty of nice Kirby games. Act Raiser (the first one) was an ingenious if simple combination of platformer and city building, hampered only by being ass bastard hard. The Chaos Engine was a really spiffy isometric shooter, made very playable by being co-op.
Any Genesis list would be incomplete without Sonic, bless his tortured license. Alien Soldier was a neato platformer in the Contra vein. Can't forget Golden Axe, dwarf FTW. The Road Rash games were some of the best pre-3D racers out there, 3 especially, if only for the way cool music. Vector Man will always have a place in my heart, for being the first game I had on the console.
Interesting tidbit about Contra: Hard Corp - it was chopped down (or was it the other way 'round?) to make Contra 3 for the SNES, but Hard Corp had far better speed and performance. However, it started as a Japanese Contra arcade game, was ported to the Master System, where it was so hard that for the only time in the series, it gained a three hit life bar. When it was released in America, they dropped the life bar but changed nothing else, making it probably the hardest of all Contras, near unplayable without an emulator.
I only had a few NES games but besides the obvious Mario titles, two really stand out. One was Iron Tank, hard top-down shooter. The other, Faxanadu - a platform RPG that, as far as I can tell, is actually endless. I've logged like 30 hours with an emulator and I don't think I'm anywhere near an end.