Each Mario is an experiment from the other, whether good or bad. It is always "Save-The-Princess-From-Bowser" in every game but the hook of each one is that the mechanics are different.
This time, You go through colorful levels with a big cape and Mario's dinosaur friend Yoshi is introduced to help Mario on his quest. He eats enemies, but he gets a different effect depending on the Koopa shell he eats. He eats a green shell and nothing happens except you roll it back. Eat a yellow shell he kills all ground enemies near him when he stomps on the ground. Eat a red shell and Yoshi shoots fireballs at enemies. Eat a blue shell and he flies in the sky.
To top that off, once you go to Star World, you will be introduced to Multi-Colored Yoshis. The Yellow Yoshis stomp groups of enemies if you eat any shell. The Red Yoshis shoot fireballs if he eats any shell. The Blue Yoshis (my favorite) fly using any shells.
Also, this game is the biggest and longest of all the Mario Games. There are big secrets that lead to different levels and switches (where you flip a switch of a color and blocks of that color appear, occasionally leading to another secret level). The secret system in this game is the hook of this game. You must defeat all of the levels and find the secrets to unlock a different version of the game (where the Koopas have big heads and Piranha Plants are pumpkin heads). Some secrets are easy while others are a bit hard. You also have to determine whether you will approach Bowser through the Front Door or the Back Door. Either way, you will throw wind-up Bowser dolls at Bowser flying in a clown copter.
The game is bigger than the games before it. The flight mechanics are more refined than in Super Mario Bros. 3. There are secrets. Yoshi is introduced.
This game gets a 10 out of 10.
PS: If you think that this game is very difficult, you ain't seen nothing' until you play Super Mario Bros. 3, which has a crooked save system, cheap enemies, big obstacles, and a bit of a bleak tone compared to the others.
Also, get the Game Boy version of Super Mario World. It has better graphics, sound, and a guide of what levels you completed (handy for finding out where secrets are).