One of the most underappriciated Mario games that would influence games to come.
First of all the Japanese SMB2 came out in Japan and was very similar to the original Mario game but developers thought that the game would be too difficult for American audiences and instead took a game called "Doki Doki Panic" and changed out the little man in a turban for Mario and friends. The Japanese version of SMB2 wouldn't come to America for years and when it did, it was in the form of "The Lost Levels" on the Mario All-Stars package.
One of the things I loved about this game was that instead of just playing as Mario, you could choose between Luigi, Peach (at the time Princess Toadstool), and Toad. Each one had different abilities. Luigi could jump high, Toad could run fast and pick up objects more quickly and everyone's favorite, Peach could float in the air for a period of time.
The story goes that Mario fell asleep and dreamed that he climbed the stairs to a door leading to a world called Subcon where a voice called him saying that their world was being terrified by a creature named Wart. Mario then awakes and tells his friends about his dream. Later, the four of them went on a picnic only to find a cave with the stairs and door as seen in Mario's dream.
The game was a departure from the classic play. Goombas and Koopas were replaced with Shyguys and Birdos. Instead of ? blocks, you had weeds. Instead of jumping on baddies, you picked them up and threw them. Items included throwing vegetables, POW blocks, stopwatches, warp potions and rocket ships. For a lot of fans, this was simply too much of a departure for the series, but I loved it.
In the end, SMB2 despite its odd place in the Mario universe, would go on to influence other Mario games. One character from SMB2, the Bob-Omb appeared in SMB3 and became a staple for the series ever since. Later on Shyguys, Birdos as well as some of the items would resurface in future games as well as an SMB2 inspired stage was used in Smash Bros.Melee.
Whatever your feelings on SMB2, it's contribution to the Mario universe is undeniable.