The best platformer games like Conker's Bad Fur Day are Banjo-Kazooie, Banjo-Tooie and Jak and Daxter. Below are 7, 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 Conker's Bad Fur Day 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 same team and the same engine, without the hangover.
Bigger, denser, and closer to Conker's sprawling set-piece levels.
The other great 3D platformer with an attitude problem, and it aged very well.
Cartoon platforming plus real weapons, which is Conker's second half.
Sharp writing in a 3D platformer, and the levels are far stranger.
The modern game most committed to being a joke and a good platformer at once.
Rare's other N64 collectathon, if you want more of the same era.
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 Conker's Bad Fur Day that are not platformer games, so they are not on this page:
The full list is on games like Conker's Bad Fur Day — 9 picks, no genre filter.
Banjo-Kazooie. The same team and the same engine, without the hangover.
No. Conker's Bad Fur Day 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 Conker's Bad Fur Day 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.