Oh wow... too many to list.. but here are some off the top of my head.
Mike Tyson's Punch-Out!!!! (NES)
Super Mario Bros. 3 (NES)
The Legend of Zelda (NES)
Super Mario World (SNES)
Super Mario Kart (SNES)
Mario Tennis (Virtual Boy)
New Super Mario Bros. Wii (Wii)
Now if you mean games that were on Nintendo platforms, but developed by companies other than Nintendo -- I could add a lot more.
Never played the first I will someday.
Favorite and only Super Mario games I've played in no particular order:
Super Mario Bros 1-3 (NES)
Super Mario 64 (N64)
Street Fighter 2 (SNES)
Donkey Kong Country (SNES)
Killer Instincts (SNES)
Super Smash Bros (N64)
Pokémon Snap (N64)
If I could only pick one it would be Super Mario World SNES. Runner up would be Super Metroid SNES. I could list 20 or 30 amazing games easily though. I still have the first issue of Nintendo Power Magazine.
All the Zelda games, and all the Mario games on all the systems, except the WII U, don't have that one. Plus, Castelvania on the original good old 8-bit original console!