Author's Saving Throw: To appease people who dislike that Goomba Stomp was removed for characters other than Mario and Luigi, there is a cheat to make that everyone can stomp.
Demonic Spiders: In addition to Lakitus and Hammer Bros., the Buzzy Beetles acquire this status due to their invulnerability to everything except the Goomba Stomp. Later versions make them vulnerable to certain special weaponsnote such as Hard Knuckle, mainly ones with limited ammunition to make up for the fact that not all characters can stomp in them (unless you actived the cheat "Anyone can stomp").
Taken Up to 11 in the most recent update with two cheat options: 'All Hammer Bros' and 'Evil Hammer Bros'. The former turns every single enemy in the game into Hammer Bros except Bowser, Lakitu (who throws Hammer Bros) and Bullet Bill Launchers (which fire Hammer Bros). The latter makes Hammer Bros chase you relentlessly throughout the entire level - even though you're sure you left them in the dust at the beginning of the level, they just keep on coming. Combine both for every platform gamer's nightmare.
Earworm: The "dubstep" remix of the Super Mario Bros. theme when you select a character - the high score music in Vs. Super Mario Bros, an arcade version (In 2.0, it only applies to the 8-bit mode). The other character select themes are pretty catchy too.
Game-Breaker: Several of the characters, owing to the fact that simple platforming levels are trivialized by putting in people who could already be considered overpowered in their own games, thus rendering most challenging spots a cakewalk:
Once Bill gets the Fire Flower upgrade in the original, he gains his Spread Gun, a rapid-fire multishot weapon that destroys bricks in one shot and fires in eight directions. Not only did this make underground levels laughably easy (just hold the fire button and walk forward), but the Spread Gun could kill Bowser in less than two seconds, and hardly anything in the game could get close while you were firing it. The Spread Gun's rate of fire was nerfed in the 2.0 update.
Before Bass came along, Simon Belmont was the other ridiculously overpowered character, with a pinpoint-accurate double jump, and (once upgraded) a Morningstar Whip that had extended range and more damage, and unlimited axes that could be thrown in front of Simon.
Sophia the 3rd comes with all of its abilities (that is to say, regenerating hovering, wall/ceiling climbing and free underwater movement), plus homing missiles. It was nerfed in 2.0 by having the climbing and hovering abilities be seperate powerups instead of innate abilities, just like in the actual Blaster Master games.
Bass. Let's recap: standalone dashing (which can be canceled into a bigger and higher jump), double jumping, autofire in seven directions with power equal to Bill's Spread Gun (and faster). All of these abilities available just by choosing him.
Or how about Fire Man? Make his attacks slightly stronger, and then make him immune to the rotating firebars that populate castle levels and the Hard Mode versions of the majority of levels?
Link's jump is easy to control and rather high, he can Goomba Stomp every enemy in the game safely (via down-thrust), and since Bullet Bills are unaffected by it, he can Goomba Springboard on them all the way to the end of the level. Jumping upward-thrusts help deal with Lakitus and Spinies. His normal thrusts, like Simon's whip, freeze enemies momentarily as you hit them, but can be spammed until they are dead. He always has the boomerang, which freezes enemies, giving you plenty of time to deal with them or use them as a stepping stone, and can also use bombs and the bow.
Samus's wave beam upgrade oscillates, can be aimed up, moves through obstacles, and reaches across the entire screen, meaning she can rapidly obliterate terrain and enemies regardless of distance, cover, or height. The only enemies impervious to this are Bullet Bills and Buzzy Beetles, and they can be taken out with missiles.
Hilarious in Hindsight: Fast-forward to Super Mario Maker, where you can scan amiibo of characters. In the Super Mario Bros. style only, Mario can become other characters upon picking up a Mystery Mushroom, and they'll function exactly like Mario. You can even put characters like Link in there as well!