Of course, there's the obligatory EVERY SONIC GAME.
Vectorman 1 and 2 (anyone else remember these)
Outrun 2019 - this sparked my interest in racing games
Gauntlet
Mortal Kombat games
Boogerman - this was so much fun when I was a kid, and to this date the only M13+ game I have ever seen (Mature 13+)
The 'Strike' series - Jungle Strike, Desert Strike, Urban Strike - these games were so cool, the forerunner to GTA games in my book because you could just decide to blow up random buildings and use rediculously powerful missles to kill a single enemy person on the ground...
Combat Cars - me and my friends had so much fun playing this game, essentially a less 'childish' mario kart
Earthworm Jim Series - how can you not love a worm in a suit that makes him look like a legitimate superhero
F-22 Interceptor - Whoo was this a fun game, I can't tell you how many hours I would play this game for, just playing dogfights over and over
The Lost Vikings - When I finally beat this game, which had I believe 40-something levels, I was so happy; this was another huge time investment, but was so much fun
NBA Jam Tournament Edition - Wow, just wow... a 2 on 2 basketball game with powerups and 'hot spots' where amounts of points from 4-9 were awarded for making the shot... so much fun with 4 people here
Primal Rage - Dinosaurs fighting... 'nuff said
Taz: Escape from Mars - Taz was my favorite Looney Toons character, so naturally I would love the video game starring him; this was a difficult game, but after awhile, you get really good at it...
Wow, what a list... I had much fun reminiscing about my earlier video game years. Feel free to criticize or contribute to a discussion of what I think was the greatest console system of it's time.