A few off the top of my head:
NES:
-Bubble Bobble
-Captain America and the Avengers (completely different game from the SNES/Genesis version)
-Contra
-Double Dragon 1-3
-Dr. Mario
-Pin-Bot
-R.C. Pro-Am
-Super Mario Bros. 1 & 3 (2 is only 1-player, but you could still take turns on levels, I suppose. Even then, SMB 1 & 3 aren't 2-player at the same time, it's 2-player on turns)
-Teenage Mutant Ninja Turtles 2 & 3
SNES:
-Captain America and the Avengers (completely different game from the NES version)
-Contra III: The Alien Wars
-Final Fight 2 & 3
-Mighty Morphin Power Rangers
-Mighty Morphin Power Rangers: The Movie
-Separation Anxiety (Spider-Man & Venom)
-Super Mario Kart
-Super Mario World
-Teenage Mutant Ninja Turtles IV: Turtles In Time