The Super Mario Bros. Super Show! episode Toad Warriors
September 25, 1989
The thirteenth episode of the Mario animated series (sixteenth also counting the Zelda episodes), broadcasted along with the live action segment "E.C. The Extra Creepy", is a parody of the movie The Road Warrior, also known as Mad Max 2, since it's set in a desert land called Car Land and has Mario, Luigi, Princess Toadstool and Toad confronting King Koopa's alter ego King-of-the-Road Koopa in car clashes. To fight Koopa, Toad uses a Starman and becomes Toad Warrior, his biker alter-ego, which is odd since for Mario and Luigi a Starman has the same use as a Fire Flower, turning them into their "Fire" alter-egos. In the next episode, "The Fire of Hercufleas", however, Toad does get fire shooting abilites when touching a Fire Flower.
This episode was originally going to be titled "The Great BMX Race 2: The Toad Warrior", being a sequel to the ninth episode, "The Great BMX Race", but it was changed likely because there are no direct plot connections between the two
Paper Mario: The Thousand-Year Door
July 22, 2004
In Paper Mario: The Thousand-Year Door, some time after uncovering the fake Zip Toad on the Excess Express, Mario receives an e-mail of thanks from the real Zip Toad. Near the end of it, he cites a line from a movie he starred in titled "The Toad Warrior": "You're cool, baby...but I'm cooler!"
"The Toad Warrior" is clearly a parody of The Road Warrior, but Zip's line doesn't seem to directly reference any line from the original movie.
It's unknown if the develpoers of the game were aware of The Super Mario Bros. Super Show! episode "Toad Warriors" and wanted to reference it, or if that's just a coincidence.
Note that Zip Toad's mail also features a reference to the movie On Golden Pond.
DiC, that created the Mario TV show, and Nintendo, that produced the games, hold no right over Warner Bros' Mad Max, in fact they only featured minor references to the movie.