The best platformer games like Banjo-Kazooie are Yooka-Laylee, A Hat in Time and Donkey Kong 64. 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 Banjo-Kazooie 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 much of the same team — the direct attempt at a successor.
The one that actually recaptured it, with better movement than the original.
Rare's own follow-on, bigger and far more indulgent about collectibles.
The template Banjo refined, and still the tightest movement of the era.
Same engine and team, aimed at a completely different audience.
The collectathon with genuinely great writing and level concepts.
A modern, straightforward take on the same structure.
Gentler and smaller, but built on the same bones.
Modern platforming with the same hand-placed, every-corner-rewards-you design.
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 Banjo-Kazooie — 9 picks, no genre filter.
Yooka-Laylee. By much of the same team — the direct attempt at a successor.
No. Banjo-Kazooie released on the Nintendo 64, 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 Banjo-Kazooie 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.