There are quite a few Mario RPG's out there to this date, such as: Super Mario RPG: Legend of the Seven Stars, Mario and Luigi: Superstar Sega, Mario and Luigi: Partners In Time, Mario and Luigi: Bowser's Inside Story, Paper Mario, Paper Mario: The Thousand-Year Door.
It depends on what you mean by role playing game.
If you mean table-top, then, sadly, the answer is "no", to the best of my knowledge, though with a little dedication, it wouldn't take too much work (comparitively) to Scrabble a gist of one together from d20 (specifically variant DnD) rules: goblins become Goombas, kobolds are Koopas with special-rules-plate-armor for their shells, and Yoshis are like dinosaurs, particularly raptors, lakitus are lizard folk on permanent cloud-chariot spells who drop summoned spikeys (Howlers reduced to tiny size and lacking their magical scream), hammer brothers are lizardfolk with +1 returning throwing hammers (like throwing axes but bludgeoning), magikoopas are low level sorcerer-kobolds (with dimension-door or something similar and wands instead of spell components), bomb-ombs are sentient alchemist fires (psicyrstal with legs stats), Bowser and family is a half-dragon turtle, while Mario and Luigi might be fighters, rangers, or rogues (don't forget plenty of skill ranks in craft [carpentry] and profession [plumber]!) and use a variety of jumping rules and feats and have weapon foci in unarmed strikes (feet from jumping) and hammers while bullet bills are... uh... something... for a quick group of ideas off the top of my head on how to do so. If the Mario brothers have a curse on them so that they're small sized when at less than half hp, magical mushrooms can, when eaten, replace potions of restoration or cure wounds, act as contengiant resurrection spells, or poison [high DC, two saves v. death] (depending on the mushroom it's meant to imitate). Most all of this info - notable exceptions being the variant jumping feats and rules, and shell-armor-things - can be found in the basic Player's Handbook, Monster Manual, and Dungeon Master's Guide. For jumping-stuff make up your own as DM or use the books Unearthed Arcana, Player's Handbook II, and Complete Warrior as suggestions. For the shell-armor, you've got to make up your own. All other power ups can (with creative reasoning) be filled in with similar already-existing magic items (Qaal's Feather Token: Flying Cape?).
It would be even easier with the 4E rules (4E is almost entirely battle-or-puzzle based outside of the comparitively rare social skill challenges) with the same ideas given above, only replacing jumping feats with fighter or rogue at-will and encounter attacks and potions with similar rituals.
If you mean role playing Video Games (RPGs), then the answer is a resounding "yes", starting with the game Mario RPG: Legend of the Seven Stars. To expand on this (in some cases 'looser' senses) there were the Paper Marios, Partners in Time, and others. A simple wikipedia search could help you with finding all the titles easily enough.
Yes, there is a real game that is a Paper Mario role-playing game. There is also a Super Paper Mario game.
RPG stands for Role Playing Game.
Mario & Luigi: Dream Team is a role-playing video game developed by AlphaDream for the Nintendo 3DS. It is the fourth entry in the Mario & Luigi series of Mario role-playing games. The game was released in Europe on July 12, 2013 and it will be released in North America on August 11, 2013.
RPG stands for Role Playing Game. MMORPGstands for Massively Multiplayer Online Role Playing Game. So, a RPG is just a role playing game, But, a MMORPGis a online role playing game.
Thy already have one. It's called New Super Mario Bros. Mii.
The Doctor Who Role Playing Game happened in 1985.
Timelords - role-playing game - happened in 1987.
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Bushido - role-playing game - was created in 1981.
Universe - role-playing game - happened in 1981.
Violence - role-playing game - happened in 1999.
Chill - role-playing game - happened in 1984.