The best arcade games like Duck Hunt are Time Crisis 3, House of the Dead: Remake and Wii Play. Below are 8, each with the reason it is here — and, at the end, what filtering to arcade costs you.
Filtering to arcade means you want short runs and a score, not a campaign. It is the right filter when what you liked was the one-more-go feeling.
What you get: A complete experience in twenty minutes, and a skill you keep. Arcade design is measured in the moment after you lose.
What made Duck Hunt worth playing in the first place is covered on the full list. This page is the arcade part of that answer, and only the arcade part.
The best of the arcade rail shooters, and the pedal is a real mechanic.
The classic light gun game rebuilt for modern hardware.
The shooting gallery mode is the closest thing to Duck Hunt made this century.
Nintendo's own target shooting, and much deeper than it looks.
The direct descendant of the whole hunting-gallery idea.
A modern rail shooter designed for a controller rather than a gun.
If you have VR, this is where the rail shooter went.
VR shooting as rhythm, and the best-feeling gun in any game.
Story and progression. Arcade games repeat on purpose, and if you want to be pulled somewhere they will not do it.
Specifically, these are strong answers for Duck Hunt that are not arcade games, so they are not on this page:
The full list is on games like Duck Hunt — 9 picks, no genre filter.
Time Crisis 3. The best of the arcade rail shooters, and the pedal is a real mechanic.
No. Duck Hunt 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.
They were designed to end. A machine that let you play for an hour on one coin did not earn its floor space, so difficulty was the business model.
Constantly, mostly by small teams. Several of the best beat-em-ups and run-and-guns of the last decade are new games built on forty-year-old design rules.
By hand. Each pick was written for the full Duck Hunt list first, on what the game actually does, and this page is the part of that list that is arcade — 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 arcade guide for where to start in the genre generally.