The best platformer games like LittleBigPlanet are Dreams, Tearaway and Yoshi's Woolly World. 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 LittleBigPlanet 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.
By the same studio, and the creation tools went from level editor to a whole game engine.
Media Molecule again, and the papercraft world is the closest thing to LBP's handmade look.
The other great yarn-and-fabric platformer, and much kinder to newcomers.
If the level editor was the point, this is the sharpest version of that idea.
Same tactile crafted aesthetic, built for playing with someone who does not play games.
The best-feeling 2D co-op platformer of that generation, with the same four-player chaos.
Yarn, physics and a two-player rope you both hang off.
For the floaty physics comedy, which is half of why LBP is funny.
The current PlayStation mascot platformer, if you want LBP's charm with tight controls.
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 LittleBigPlanet — 9 picks, no genre filter.
Dreams. By the same studio, and the creation tools went from level editor to a whole game engine.
No. LittleBigPlanet released on the PlayStation 3, 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 LittleBigPlanet 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.