It is fun because it's poorly balanced.
Yoshi is another success factor. Not only is he really cute, he can eat your enemies for you and by eating different kind of koopas he gain different abilities. When he has a blue shell in his mouth he can fly, with a red shell he can shoot fireballs and with a yellow one he can kill enemies by stomping the ground.
In super Mario World you have one large overworld map and several save points along the way. The normal levels are yellow if there is only one exit and red if there is a secret. However there are also ghost houses, towers and switch palaces (which are used to turn on blocks of a certain colour). Perhaps the biggest of all Super Mario World's success factors is how fun it is to find the secrets, which are in very many levels. Those secrets often require a lot of skill and sometimes can't be taken without a cape and/or Yoshi, The secrets unlock a different path on the overworld map, so you can choose multiple paths to get through the game, but most fun of all is to try to find all the paths. Here, the ghost houses make it particularly hard. Often finding the normal exit in a ghost house can be challenging enough.
Like I said, the game has a few flaws that somehow actually make it better. Pretty early in the game you can find a secret way and get to a "shop". This shop doesn't cost anything, but you get five blocks, with a Yoshi in one, feathers (which gives you the cape) in two and fireflowers in two. You can visit the shop as many times as you like, even without visiting a level in between. When you take the block with the Yoshi and you already have Yoshi, you get a 1-up instead. In other words, no matter where you are in the game you can always backtrack to the shop and get a Yoshi, two capes and as many lives as you want. This could of course be counted a flaw, but in one way it just adds an easier difficulty. You can still choose to ignore the shop and get more challenge out of the game if you prefer.
The game has a lot of great level design and a lot of variety, from normal levels where you stomp the koopas to levels where you ride on platforms and try to avoid spinning sawblades to caves where you try to avoid being charged by Jockeys. That's right, jockeys. One of the most common enemies in the game are American football players that either dash at you, jump at you or throw baseballs or American footballs at you. It is a bit weird, particularly since they look perfectly human, unlike every other Mario enemy ever, but it doesn't matter. Both the game's music and artstyIe gives it such a silly feel to it that I don't care.
The game has a lot of simple and often silly fun and I can only think of a couple of flaws that doesn't work to it's favour. One is that a few of the boss fights are just the exact same boss in the exact same place doing the exact same thing. The other is that playing the game with the GC controller means that I will often have to hold down Y and press B, which means I have to hold the control pretty awkwardly since it is more natural to use your right thumb for both of those buttons. All in all though, those flaws are not so major and this game definitely seems like it's immune to the years that have passed since its first release.