Super Mario World was the game that came with the Super Nintendo, released in 1990. Super Mario World added onto the additions made by Super Mario Bros. 3, replacing the Leaf with the Feather, the tail with a cape, and having the ability to explore the full map of the game. You can revisit any level you've already completed (with the exception of castles unless you use a secret button code) and there are multiple exits in many levels which allow you to build different paths through the game. The game also has a save system.
Possibly the most important introduction of the game was Yoshi, a dinosaur coming in multiple colors that was subsequently thrown into as many Nintendo games as humanly possible. Yoshi made the game far too easy, being able to take hits for you and other such nonsense.