The best platformer games like Super Mario World are Yoshi's Island, Super Mario Bros Wonder and Donkey Kong Country 2. Below are 9, each with the reason it is here — and, at the end, what filtering to platformer costs you.
Filtering to platformer means you want the movement itself to be the pleasure. It is the right filter when the thing you liked was getting from one place to another.
What you get: A game you can judge in ten seconds. Platformers live or die on the jump, and a good one feels right before anything else happens.
What made Super Mario World worth playing in the first place is covered on the full list. This page is the platformer part of that answer, and only the platformer part.
The direct follow-up, and the most inventive platformer on the SNES.
The modern 2D Mario, and the closest in spirit to World's playfulness.
The other SNES platformer with hidden exits and a secret world.
If the level design was the appeal, this is infinite.
The most polished 2D platformer since.
The best-feeling modern platformer, with a hidden B-side for every level.
The NES peak, and much of World grew out of it.
Deliberately retro, but with a modern sense of fairness.
The other pillar of SNES platforming.
Weight. Platformers rarely carry a story you will think about afterwards, and the collectible-led ones can become checklists if you let them.
The full list is on games like Super Mario World — 9 picks, no genre filter.
Yoshi's Island. The direct follow-up, and the most inventive platformer on the SNES.
No. Super Mario World released on the Super Nintendo, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Whether the move set is complete early. The great ones give you everything in the first level and spend the rest asking better questions of it; the weak ones drip-feed abilities to disguise thin level design.
Different games. 2D platformers are about precision on a single screen; 3D ones are about reading space and camera. Each pick below says which it is.
By hand. Each pick was written for the full Super Mario World list first, on what the game actually does, and this page is the part of that list that is platformer — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the platformer guide for where to start in the genre generally.