This page explains in detail the interactions between the Doraemon series and the Mario series.
Shogakukan Kindergarten[]
UNDIRECT: October 1987
Doraemon
Mario
Doraemon and Mario appear together in an illustration on the October 1987 issue of this children's magazine. Various characters from the two series, as well as Little Ghost Q-Taro are seen running a marathon wearing Mario's hat, with Mario himself waving a white flag.
Since this just shows the characters performing an activity, without much narrative value, it's arguable if it should be considered a link. (see the Cover rule)
We consider it a link because it's a plausible scenario that can be considered to happen in a fictional universe.
Super Mario-Kun[]
2005
Doraemon
Mario
Doraemon makes a small cameo alongside various random characters in an issue of Super-Mario Kun based on Paper Mario: The Thousand-Year Door.
He's later shown alongside Mario characters in a small image on issue 42 (April 28, 2015). This is likely done to celebrate Super Mario-Kun surpassing Doraemon as the longest running comic on the CoroCoro magazine.
Rio 2016 closing ceremony[]
UNDIRECT: August 21, 2016
Doraemon
Mario
During the closing ceremony for the 2016 summer olympics, the section "Warming up! Tokyo 2020" served as a presentation for the next Olympics. During this section a clip was shown featuring various anime and video game characters, such as Hello Kitty and Pac-Man. During this clip, Prime Minister of Japan Shinzo Abe is shown transforming into Mario and meeting Doraemon, who brings out of his pocket a Warp Pipe allowing the Prime Minister as Mario to reach Rio.
While the closing ceremony is a non-fictional event, this clip can be considered an undirect link between the two series, since the two characters interact; this doesn't apply to the other featured characters, since they're each shown in a separate part of the clip, and are not interacting with one another.
The type of link is arguable, since the Mario character is actually Prime Minister Abe in disguise (the only notable difference is the writing "Tokyo" on his cap, rather than Mario's "M").
License[]
Both Super Mario-kun and Doraemon were published by Shogakukan on the CoroCoro magazine, so they could include references between the two comics.
The respective owners licensed the characters to use on the Rio 2016 closing ceremony.