The best platformer games like Sly Cooper are Sly 2: Band of Thieves, Jak and Daxter and Ratchet and Clank. Below are 6, 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 Sly Cooper 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 sequel opened it up into full heist missions and is the best of the three.
Same era, same studio family, same PS2 cartoon craft.
The third pillar of the PS2 mascot trio, and the most mechanically generous.
Stealth made readable and fair, with the same forgiving spirit.
Puzzle stealth, quick to restart, never punishing.
For the rooftop traversal, if movement was the real appeal.
Weight. Platformers rarely carry a story you will think about afterwards, and the collectible-led ones can become checklists if you let them.
Specifically, these are strong answers for Sly Cooper that are not platformer games, so they are not on this page:
The full list is on games like Sly Cooper — 9 picks, no genre filter.
Sly 2: Band of Thieves. The sequel opened it up into full heist missions and is the best of the three.
No. Sly Cooper released on the PlayStation 2, 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 Sly Cooper 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.