Quite possibly the pinnacle not only of Super Mario, but of all platforming games ever.
Mario's first 16-bit adventure starts off on Yoshi's Island, where Mario, Luigi, and Princess Toadstool are having vacation or something. None of that really matters, though, as right off the bat Bowser himself comes and kidnaps our fair monarch. It's up to the superior plumber siblings themselves (with the help of their new dinosaur buddy Yoshi) to save the princess, rescue the scattered Yoshi eggs being held by Bowser's seven Koopalings, and return peace to the entirety of Dinosaur Land.
The game contains 7 areas to traverse (and a couple of secret areas, hush hush), from the tranquil Yoshi's Island to the dark caverns of the Vanilla Dome to the confusing and haunted trails of the Forest of Illusion. Each has several paths you can take to reach the castle where one of the Koopalings waits with a Yoshi egg in tow. There's a variety of level types that you'll pass through in the game, from basic field levels to underground to underwater and even some levels in the sky. The variety helps keep the game fresh as you seek to save the princess, and the sublime level design makes the game just a joy to play through. Seriously, it never gets old, even decades later, and it's a testament to Miyamoto and his team's skill at creating brilliant levels for the gamer to discover.
To help you through the levels and the myriad different and interesting obstacles you'll have to overcome, Super Mario World returns the familiar Super Mushroom and Fire Flower power-ups while adding one new one: the Feather, which grants you a cape to fly over levels with. It also sees the introduction of a new Mario character who has since gone on to become a fan favorite: the prehensile-tongued green dinosaur Yoshi. Mario can find Yoshi eggs in ? Boxes scattered around Dinosaur Land. Out from the egg bursts a full grown Yoshi to ride, who can use his tongue to eat enemies and can take a hit before running off scared, at which point you can try to catch him.
The game controls like a dream. The Feather can take a bit to get used to when trying to fly, but everything else is intuitive and responsive like it should be. With the increased button count on the SNES controller, Mario even has a new skill: the spin jump, which can be used to shatter blocks and crush some of the more resilient enemies. It's what you'd expect from a Mario game: it's tight, and even when you want to blame the game for your screw-ups, you know deep down inside it was all your fault.
As for the graphics, they pale in comparison to later SNES masterpieces, but as an early SNES game, it's fantastic and features some nice effects. There may be no Mode 7 like F-Zero or Super FX chip like this game's sequel, Yoshi's Island, but what's there is beautiful and fits the look well. Something similar can be said for the musical score. There's some excellent and memorable tracks on this one (the Castle Theme can get stuck in your head for weeks), and it fits the game to a T.
All-in-all, everything in Super Mario World is fantastic, and Miyamoto and crew did a wonderful job bringing it all together into a masterpiece of a game that has stood the test of time. Mario fans may debate which game is better, this or the also-amazing Super Mario Bros. 3 (me being on the side of World), but none deny that this game is a fantastic game that deserves the heaps of praise it receives. It's one of the games that just should be required to be played if you're a fan of video games, and it's a game that can make you remember why you love playing video games in the first place. It's one of (if not the) high point of the Mario series, of platformers, and of all video games.