This page explains in detail the interactions between the Mario series and the Nightmare on Elm Street series.
Freddy's Nightmares episode Missing Persons[]
Three screenshots from the scene.
May 6, 1989
Mario
Nightmare on Elm Street
At the beginning of the nineteenth episode of the Nightmare on Elm Street TV series, two children are seen playing World 1-2 of Super Mario Bros., before the new baby sitter blocks their view of the television. Curiously they seem to be both playing at the same time, while the actual game doesn't feature two player simultaneous gameplay (and only one player character is shown on the TV in the episode).
Freddy's Dead: The Final Nightmare[]
Spencer about to jump into the orange pipe.
September 13, 1991
Mario
Nightmare on Elm Street
In the movie Freddy's Dead, a character named Spencer ends up within a video game while dreaming. In it there are some references to the Mario games, most notably an orange pipe very similar to Mario's warp pipes.
This count as a type 2.5 link because even if Spencer physically interacts with the elements of the game, that's still just a game within a dream within the movie.
Super Mario in Die Nacht des Grauens - Part 1[]
A detail of the fifth page of the comic, showing the shadow of a Freddy look-alike.
may 1996
Mario
Nightmare on Elm Street
In the special Halloween episode of the Super Mario comic published on the german Club Nintendo magazine, in a scene where Mario, Link from the Zelda series and Kirby from his own series fight many monsters, a shadow of a person resembling Freddy Krueger can be seen. He's wearing a long sleeved shirt, a hat and a pair of bladed gloves, corresponding to Freddy except that he only wears one glove. (see Super Mario in Die Nacht des Grauens cameos for more)
License[]
Mario's copyrights owner (Nintendo) and Nightmare's copyrights owner (New Line Cinema) had no right over the other series' elements, in fact they've only been able to do subtle references. In Freddy's Nightmare the game shown is actually Super Mario Bros., but since it only appears for a few seconds, they probably didn't need a license to use it.