Nintendo made a lot of sequels for it's main franchise games. Some were great, some were bad.
Super Mario Bros. 2 was released by Nintendo in 1988. It's a follow up to the original Super Mario Bros. released in 1985. However, we all know how convoluted the story is. The real Mario 2 was not released in the US, as it was deemed too hard. It would NOT be released until Super Mario All-Stars as the Lost Levels. This game, was a redesigned game on the Famicom called Doki Doki Panic.
Despite this, a lot of concepts from Mario 2 have been reused in later entries. Such as the Shy Guy, Birdo, the POW block and the ability to pick up and throw enemies. Sure, many fans disliked the ending of it being a dream, but what we have here is a decent platformer with some great characters with different abilities.