The best casual games like Katamari Damacy are We Love Katamari Reroll, Donut County and Untitled Goose Game. Below are 7, each with the reason it is here — and, at the end, what filtering to casual costs you.
Filtering to casual means you want something you can put down. That is the whole definition, and it says nothing about how deep the game is.
What you get: A game that fits around a life. Short sessions, save anywhere, no penalty for a week away.
What made Katamari Damacy worth playing in the first place is covered on the full list. This page is the casual part of that answer, and only the casual part.
The sequel, and the better of the two.
A hole instead of a ball, and the same escalating-size comedy.
Same deadpan mischief and the same small, perfect scope.
Strange, funny systems under a friendly surface.
Small, warm, and finishable in an evening.
By Katamari's designer, and even stranger.
A bright systems game hiding under a children's surface.
Momentum, sometimes. A game designed to be left is also a game that is easy to forget you were playing.
Specifically, these are strong answers for Katamari Damacy that are not casual games, so they are not on this page:
The full list is on games like Katamari Damacy — 9 picks, no genre filter.
We Love Katamari Reroll. The sequel, and the better of the two.
No. Katamari Damacy released on the PlayStation 2, 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.
No. Several of the deepest games there are — Tetris, Balatro, Into the Breach — are playable in twenty-minute pieces, and some of the shallowest demand an entire evening.
Often the opposite. Many are built around daily timers and streaks, which means stopping does cost you — the one thing a casual game is not supposed to do.
By hand. Each pick was written for the full Katamari Damacy list first, on what the game actually does, and this page is the part of that list that is casual — 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 casual guide for where to start in the genre generally.