The best rpg games like Paper Mario are Paper Mario: The Thousand-Year Door, Bug Fables and Mario and Luigi: Bowser's Inside Story. Below are 9, each with the reason it is here — and, at the end, what filtering to rpg costs you.
Filtering to RPG means you want progression — a character to build or a party to grow — layered on top of whatever else you liked.
What you get: A reason to keep going after the novelty wears off. RPGs are the genre that reliably converts hours into feeling more capable.
What made Paper Mario worth playing in the first place is covered on the full list. This page is the rpg part of that answer, and only the rpg part.
The peak of the series, and the remake is faithful.
An indie Paper Mario, and better than it has any right to be.
The other Mario RPG line, and the best-written of them.
Where the timed-hit idea started, and the remake is good.
Timed hits in every battle, with a much bigger story.
Turn-based battles where dodging is a real-time skill.
Short, funny, timed-hit RPG for the same audience.
The best-paced turn-based RPG there is.
The other funny turn-based RPG people never stop asking about.
Immediacy. Almost every RPG asks for a slow first few hours, and the systems that make hour forty good are the same ones that make hour one a menu.
The full list is on games like Paper Mario — 9 picks, no genre filter.
Paper Mario: The Thousand-Year Door. The peak of the series, and the remake is faithful.
No. Paper Mario 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 stats are the point. In an RPG the build decides what you can do; in an action game with stats the build only decides how fast you do it.
No. The picks below span turn-based, real-time and action RPGs, and each one says which it is.
By hand. Each pick was written for the full Paper Mario list first, on what the game actually does, and this page is the part of that list that is rpg — 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 rpg guide for where to start in the genre generally.