Just straight up platformer.
Super Mario Bros. So good in every possible way, my favorite Mario as well. Lost Levels is a good challenge once you feel you've done everything you possibly can in SMB. We all played it when we were kids and played the shit out of it, so it's a good come back where you can get your reflexes back, you know you still remember all the tricks, shortcuts, moments where you can just hold that B button and go! So much greatness, the way Mario moved was awesome, he slides perfect, the break sounds good, you catch everything on the fly, so intuitive, for me there's hardly anything better.
Super Mario World is also amazing but I feel that like SMB3 it just started to slow down, 3 and SMW share these moments that break up gameplay in favor of bonus stages, maps, and tons of secrets which is cool but sometimes you find yourself just running safely just for the sake of flying and picking coins, I lot of the time you spent looking for secret stuff and unlock everything, I liked it but I always found the gameplay of the first SMB so much more dynamic.
Action Platformer, well there's no better than Ninja Gaiden III NES but I'm not sure if that will count in this thread. So many good ones though, Ninja Spirit PCE/Arcade, BATMAN (Sunsoft City) NES is also excellent and of course Megaman 2, there's also Bionic Commando NES. NES is definitely the best console for action platformers, of course there are tons of disasters but the good ones are just straight up gems. Castlevania is in a league of its own being the true first of its kind which basically spawned a genre. Superb game, fantastic music.
Then there's the one screen ones, I really like Nightmare in the Dark, it's probably my favorite but Donkey Kong is always great to play, also Bang Bang Busters is a lot of fun, way more fun than I ever thought it would have been. I'm a sucker for this genre of platformers 'cause I started with Game & Watch and a lot of this games were at the arcades, like DK, Joust, Popoye, of course Pac-Man and stuff but I could play DK Jr. and the Mickey's Firehouse was awesome with Game & Watch. Hell my first game I ever got to play was Parachute Game & Watch, amazing addictive crazy fucking game, insane! The DS had 2 Game & Watch collections and they are way better than the GB/GBC/GBA ever could reproduce, I play these games on my original DS 'cause of the reflective LCD screen and it brings that authentic feel which is so great, the graphics look like LCD stencils, amazing! They mix Octopus and Parachute together, the game is insane, they even added multipliers which bring so much more fun and eagerness to score high.
SNES was a great system and I wish I knew more about the games for it but at the time it came out I was all about arcades and arcade ports, the NES was in some ways better than the arcade back in the day, Contra NES> Contra Arcade, the same could be said about the sequel and Life Force but I'm getting way out of topic here. I'd like to see some SNES recommends, I have the usual suspects.
I never quite Kirby a shot until recently and then it was a rude awakening 'cause some of these games are actually really good, the GBA Nightmare in Dreamland was great. I have a few here and there not all. I heard good things about Tomba and Klonoa but I have yet to try those games.
The New Super Mario Brothers Wii U is pretty awesome, all those challenges are ridiculous, Nintendo is giving a little for everyone that likes Mario for very different reasons. I'm not a fanboy but I like the games.
My love is with NES, I could do with just that console for the rest of my life, everdrive...I'm all set.
My favorite Action platformers in no particular order
Ninja Gaiden III NES
Ninja Spirit PCE/Arcade
BATMAN (Sunsoft City) NES
Super Mario Bros. NES
G.I. Joe Taxan NES
Castlevania NES
Ninja Gaiden I & II NES
Megaman 2 NES
Bionic Commando NES
Super Mario World SNES
Super Castlevania IV SNES
Castlevania Rondo of Blood Turbo Duo
Super Ghoul n' Ghosts SNES
Hagane SNES
Cannon Dancer/OSMAN Arcade
Shadow of the Ninja NES
Ninja Five-0 GBA (Prolly one of my favorite games ever)
Kabuki Quantum Fighter NES (Thank you Lonesage, I got to No Death Run that sucker, I know it's not hard but still.)
I could keep going...
