The best platformer games like Aladdin are The Lion King, Castle of Illusion and DuckTales. Below are 10, 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 Aladdin 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.
Same era, same approach to animation, and considerably harder.
The Genesis Disney platformer that got the controls right first.
The NES Disney platformer everyone still names, and the pogo stick is why.
Two-player Disney platforming built for a child and an adult together.
The other Genesis game built to show off hand-drawn animation, by some of the same people.
The Genesis platformer to compare everything else on the system against.
The modern version of this idea, and the animation is still the point.
Hand-animated action platforming with combat that goes deeper.
If the era rather than the animation is what you are after.
Where the hand-drawn-cartoon-as-a-game idea ends up, and it is brutal.
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 Aladdin — 10 picks, no genre filter.
The Lion King. Same era, same approach to animation, and considerably harder.
No. Aladdin released on the Sega Genesis, 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 Aladdin 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.