13. Super Mario Bros. 2
Fun Fact: Super Mario Brothers 2 began development as an entirely different game called Doki Doki Panic that had nothing to do with Mario whatsoever!
Super Mario Brothers 2 took a very different approach to the series, owing to the quirks of its development. Players could now choose one of four different characters, each of whom had their own characteristics. Mario was a balanced choice, Luigi's jump was farther and held him in the air for longer, Princess Toadstood could float, and Toad was the strongest.
Toad's ability came in handy because there was a lot of stuff to pull out of the ground in Super Mario Brothers 2. It was one of the core mechanics added to the side-scrolling platform play of the first game. Players would have to yank vegetables out of the ground and throw them at enemies.
The game also had a strange mechanic where players could throw a magic potion on the ground and open a door into an alternate mirror-version of the world where everything was dark as night. That's where players would find the coins that granted extra lives. The game also featured a life meter for the first time, and used hearts as the currency by which the meter could be refilled.
The incongruous nature of Super Mario Brothers 2 as compared to other games in the Mario series could always be explained by the end of the game, where the entire adventure is revealed to be nothing other than Mario's dream.