Super Mario Bros - There's nothing like the classics...
Until you see the classics have become horrific abominations of what was-
Super Mario Bros: The Lost Levels - An official ROM hack? Oh, Nintendo. Only the Ground. back-ground objects, Semi-Solid Platforms, Brick Blocks, and select Mushroom Platforms were changed.
Super Mario Bros Special - The ORIGINAL sequel, this iteration is based on the Sharp X1 version, and uses standard scrolling, instead of flip-screen. The
horrendous original music and graphics of the original Special are retained, with some new remixes. The SMB1 physics are kept, though.
All Night Nippon Super Mario Bros - FOUR versions of the original SMB before 16 bit. FOUR! This is The Lost Levels graphics, except with Toads and enemies being replaced with Japanese celebreties for comedic effect.
Super Mario Bros. 2 - By popular demand, it's in! SMB2, where you throw stuff at more stuff. The Lost Levels was hard enough to not be released outside Japan until All Stars, but SMB2 is TOUGH!
Doki Doki Panic - SMB2's original form. You played as the Yume Kojo characters Imagine, Mama, Lina and Papa instead of Mario, Luigi, Peach and Toad. The game also contains different, non-Mario graphics for the Shell, Magic Potion, Mushroom, 1-Up Mushroom, Phantos and Mask Gates, as well pallete changes and animation additions.
Super Mario Land - Mario? Portable? SIGN ME AND THE REST OF AMERICA UP! This game was CLOSE to the originals, but is lesser known. Hey, at least we have Bill Blaster pipes! Also, Daisy. Also available in glorious color.
Super Mario Bros. 3 - The next game, SMB3 is quite a charm! Several power-ups, Koopalings, Airships, and more! Also, it introduced slopes.
Super Mario All-Stars - All 3 games in 16 BITS! All we need is BLAST Processing.
Super Mario World - Needs no explanation. Fine. Cape Feather, Chargin' Chucks, Sunken Ghost Ship, Yoshi.
SMW 8-bit - A decent bootleg. Yeeeup! a bootleg mixed in with the real stuff. So sue us.
Super Mario Land 2 - Mario? Portable? Again? Like the console games? But on the go? WELL SIGN ME AND THE REST OF (AMERICA/NORTH AMERICA/EARTH) UP! Far closer to things like SMB3 and World, Super Mario Land 2 is a fair sequel. Also, Bunny Carrot. And Wario. Wah. And you can play in color. Woot.
Super Mario World 2: Yoshi's Island - The prequel to the rest of the series, Yoshi's Island is less of a sequel to World, but rather advertised as that to ride off World's coattails. Hey, it's fun. Also, try not to lose that pesky baby Mario.
Super Mario Advance Series - GBA Remakes of Super Mario Bros 2, World, Yoshi's Island and 3 in that order. Should we count Super Mario Bros. Deluxe as Super Mario Advance 0?
Super Mario Bros. Deluxe - Very close, but several sprites are different/animated.
New Super Mario Bros. - After a 2D Mario drought, New Super Mario Brothers brought us back to the series' roots. Also, old things such as Goal Poles, Secret Exits, colored Koopas, climbing, Cheep Cheeps, etc. Famous power-ups like the Mega Mushroom, Mini Mushroom, and Blue Shell return in 3D Maker. HOORAY!
Yoshi's Island DS - More babies. different soundtrack. Time-warping Bowser. Baby-dependant Yoshi abilities. Two boss Burt Bros. Super-big Tap-Tap. Good.
New Super Mario Bros. Wii - The 2D Wii Mario game, NSMBW is also pretty good. However, this is before Nintendo was REALLY milking the series. Also, Propeller Mushroom and Penguin Suit.
New Super Mario Bros. 2 - Less about saving Pech, and more about the MONEY! There's the Raccoon Leaf, Mini Mushroom, Mega Mushroom, Gold Flower, Fire Flower, Super Mushroom, and gold Brick Block that goes over your head and spits money.
New Super Mario Bros. U - Flying Squirrels. Baby Yoshies with powers. That's about it.
Super Mario Bros. E3 2014 - The Super Mario Bros. style of the Super Mario Maker E3 2014 demo.
New Super Mario Bros U E3 2014 - The NSMBU style of the Super Mario Maker E3 demo. These two play almost identical. However, you can wall jump in this one.
Super Mario 64 - N64 classic. Not much else can be said.
Super Mario Sunshine - A fair deviation from the original formula. You've got Fludd, juice-spitting Yoshis, and an oh-so-mysterious book in a bottle.
Super Mario 64 DS - Nintendo's trend of re-releasing old games contunues with this DS port of the N64 one. Also, Yoshi. Luigi. Wario.(UNDER CONSTRUCTION)