Oh, god. I can't even think of where to start. Punch Out, any Ninja Turtles game, especially 2 and onward If you see a game called Trog! snatch it up, I've been trying to find a copy for a while now. It was a sleeper hit. Any Mario, Mega Man or Zelda, of course. Final Fight
Honestly, I would just start grabbing cheap games by the handful and give them a try. There's a lot to discover and the prices are kind of random, a more expensive game isn't always a better one so just buy a lot of cheap ones.
Get Crash n' the Boys Street Challenge. It's got the characters from River City Ransom it it. Get that too. Get Uninvited, Dejavu, Shadowgate, Maniac Mansion, Double Dragon 2, SMB3, Mike Tyson's Punch Out, Solar Jetman, Elevator Action, and Zelda.
Super Mario Bros. 3 Mike Tyson's Punch-Out!! Kirby's Adventure Star Tropics Star Tropics II: Zoda's Revenge Mega Man 2 Mega Man 3 Bionic Commando Gargoyle's Quest 2 Ducktales Darkwing Duck Contra Super C Castlevania Castlevania III: Dracula's Curse Gradius Lifeforce Teenage Mutant Ninja Turtles II: The Arcade Game Teenage Mutant Ninja Turtles III: The Manhattan Project Double Dragon Double Dragon II: The Revenge Ninja Gaiden Ninja Gaiden II Blaster Master Batman Crystalis The Guardian Legend
Felix the Cat Super Mario Bros Contra Super C Castlevania and Castlevania III Duck Tales 2 Bonk's Adventure Little Samson Teenage Mutant Ninja Turtles III Ninja Gaiden and Ninja Gaiden III Metroid Legend of Zelda Mega Man II and Mega Man IV and Mega Man VI Mighty Final Fight
I'm sure there are more, probably some real obvious ones, but they aren't coming to me at the moment