The best shooter games like Star Fox 64 are Sin and Punishment: Star Successor, Panzer Dragoon Orta and Rez Infinite. Below are 8, each with the reason it is here — and, at the end, what filtering to shooter costs you.
Filtering to shooter means you want the guns to be the answer. It is the right filter when what you liked was the feedback — the sound, the recoil, the way enemies react.
What you get: Moment-to-moment feel, and the shortest distance between picking a game up and enjoying it.
What made Star Fox 64 worth playing in the first place is covered on the full list. This page is the shooter part of that answer, and only the shooter part.
Treasure's rail shooter, and the closest thing to a spiritual sequel.
The other great rail shooter, and visually still remarkable.
Rail shooting reduced to rhythm and light.
An indie game made explicitly to be Star Fox 64 again.
The most recent entry, if you can get on with the controls.
Arcade-length space missions with the same replay-for-medals structure.
If the dogfighting was the appeal and you want it open.
Rail shooting on foot and in the air, with the same chatty tone.
Variety. Shooters commit hard to one loop, and the ones that try to be something else usually do the something else badly.
Specifically, these are strong answers for Star Fox 64 that are not shooter games, so they are not on this page:
The full list is on games like Star Fox 64 — 9 picks, no genre filter.
Sin and Punishment: Star Successor. Treasure's rail shooter, and the closest thing to a spiritual sequel.
No. Star Fox 64 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.
How the guns sound and how enemies react to being hit. A shooter with mediocre levels and superb weapon feedback is more fun than the reverse, every time.
Each pick says. Several of the best shooters ever made are single-player campaigns, and a few of the co-op ones are genuinely worse with bots.
By hand. Each pick was written for the full Star Fox 64 list first, on what the game actually does, and this page is the part of that list that is shooter — 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 shooter guide for where to start in the genre generally.