The best rpg games like Mario and Luigi Superstar Saga are Mario and Luigi: Brothership, Mario and Luigi: Bowser's Inside Story and Paper Mario: The Thousand-Year Door. 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 Mario and Luigi Superstar Saga 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 most recent entry, and the timing system is intact.
The best-written game in the series.
The other Mario RPG line, and the remake is excellent.
An indie Paper Mario, and better than it has any right to be.
Timed hits in every battle, with a much bigger story.
Where the timed-hit idea started, and the remake is faithful.
For the timed-input combat, in a far more serious game.
Turn-based battles where dodging is a real-time skill.
The other funny turn-based RPG that 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 Mario and Luigi Superstar Saga — 9 picks, no genre filter.
Mario and Luigi: Brothership. The most recent entry, and the timing system is intact.
No. Mario and Luigi Superstar Saga released on the Game Boy Advance, 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 Mario and Luigi Superstar Saga 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.