The best shooter games like Contra are Contra III: The Alien Wars, Metal Slug 3 and Cuphead. Below are 9, 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 Contra 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.
The SNES entry, and the high point of the series.
The most generous run-and-gun ever made, and superb in co-op.
Boss-pattern run-and-gun with the same one-hit tension.
Made specifically to be Contra again, and it succeeds.
Treasure's Genesis run-and-gun, and mechanically richer.
The modern remake, and a solid entry point.
Destructible run-and-gun chaos, four players, very funny.
A polished modern arcade run-and-gun with great co-op.
One-hit-kill run-and-gun with a cartoon look.
Variety. Shooters commit hard to one loop, and the ones that try to be something else usually do the something else badly.
The full list is on games like Contra — 9 picks, no genre filter.
Contra III: The Alien Wars. The SNES entry, and the high point of the series.
No. Contra released on the Nintendo Entertainment System, 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 Contra 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.