Lemme think... There's always the Contra games. Bionic Commando is a good one too. Ghosts n' Goblins, Journey to Silius, Little Nemo, Little Samson, the Mega Man games, Metal Storm is a cool one with some great pixel art, Power Blade, the list goes on and on. Those are all just NES games too.
Here's some of my favorite SNES ones, Act Raiser (although half the game is like Sim City), Super Castlevanina 4, Contra 3, Donkey Kong Country, Hagane, Indiana Jones' Greatest Adventures, the Super Star Wars games, Mega Man X, The Ninja Warriors (although it is more of a beat em' up), Run Saber, Sky Blazer, Sparkster, Sunset Riders, Super Ghouls n' Ghosts, and the Super Turrican games. I'm sure there's more I'm not thinking of...
The Sega Genesis has some awesome ones as well! Alien Soldier, Comix Zone, Castlevania Bloodlines, Contra Hard Corps, Dynamite Heady, Mega Turrican, Shadow Dancer, Rocket Knight Adventures, Gunstar Heroes (a must play),The Sonic the Hedgehog games, the Shinobi games (especially Shinobi 3), and you can't forgot Strider.
So there's a few. There's at least a handful of great action platformers for every console, let me know if you want any other suggestions, haha.