This page explains in detail the interactions between the Mario series and the Three Men and a Baby series.
The Super Mario Bros. Super Show! episode Two Plumbers and a Baby[]
October 02, 1989
Mario
Three Men and a Baby
Super Mario Bros. Super Show Episode 21 - Two Plumbers and a Baby & Lost Dog
The full episode.
The title of seventeenth episode of the Mario animated series (twenty-first also counting the Zelda episodes) as well as part of its plot are based on the movie Three Men and a Baby.
It's about Koopa's alter-ego King Goo Goo Ga Ga Koopa using a magical fountain of youth to turn the inhabitants of the Kingdom of Youth into babies and enslave them, while Mario, Luigi, Princess Toadstool and Toad try to stop him. The Princess, however, falls into the fountain and turns into a baby herself, so Mario, Luigi and Toad have to look after her, while figuring out how to stop Koopa. In the end they manage to defeat him by making him fall into the fountain as well, turning him into a baby, and are able to change the princess and the other inhabintants back by reversing the flow of the fountain.
Notice that the episode technically features the first appearance of Baby Bowser, that would later appear in Yoshi games (see Mario X Yoshi#Super Mario World 2: Yoshi's Island), as well as Baby Peach, that would later appear in Mario & Luigi: Partners in Time. This episode's baby Koopa also appears in the eighth episode of The Adventures of Super Mario Bros. 3 called "Toddler Terrors of Time Travel".
License[]
DiC, that created the Mario TV show, holds no right over Disney's Three Men and a Baby, in fact they only featured a minor reference to the movie.