Mario

Mario is the main and titular protagonist of Nintendo's flagship Mario franchise, and he is the mascot of Nintendo by extension. Mario has appeared alongside Samus Aran on various occasions, especially within the Super Smash Bros. series, and has sometimes made a cameo appearance in Metroid-related media.

Victory Techniques for Metroid
In the manga Victory Techniques for Metroid, Samus Aran comes across an Air Hole and immediately mistakes it for a Warp Pipe. She imagines Mario (whose design resembles his Super Mario Bros. sprite) entering the Air Hole, but when Samus enters it, she is immediately launched out by a Zeb.

Metroid Prime 3: Corruption
If one plays Metroid Prime 3: Corruption while having save files on Super Mario Galaxy or Super Paper Mario, the game grants Ship Bumper Stickers modeled after Mario's emblem and Paper Mario's head, respectively.

Metroid Prime: Federation Force
While Mario does not appear in Metroid Prime: Federation Force, a Paint Job with the "M" emblem can be unlocked in the Blast Ball mode by scanning any of Mario's amiibo.

Super Mario Bros. 3
In Super Mario Bros. 3, when using a Starman, Mario or Luigi can perform a somersault jump that resembles Screw Attack.

Mario vs. Wario
In the Mario vs. Wario Nintendo Power comic, Peach desires a different Samus Doll that she expressed was cute, so Mario and Wario fight each other to buy the doll for her. In the end it turns out that Luigi had bought it before them.

Super Mario RPG: Legend of the Seven Stars
In Super Mario RPG: Legend of the Seven Stars, Mario can meet Samus sleeping in the Mushroom Castle's guest room bed if Mario returns before going to Land's End. If Mario talks to Samus, she tells him that she is resting up for Mother Brain.

Tetris (Nintendo Entertainment System)
Beating Game B on different difficulty levels earns an animated ending screen featuring various Nintendo characters playing musical instruments, including Samus Aran and Mario.

F-1 Race
Along with various women, Mario appears cheering for the player before Course 6.

Super Smash Bros. series
Mario, like Samus, is a playable fighter in every installment of the Super Smash Bros. series.

Super Smash Bros. Ultimate
In Super Smash Bros. Ultimate, Mario is slightly redesigned to take into account his appearance in Super Mario Odyssey, including having his cap appear as Cappy.

In 04: Samus, Mario and Luigi attempt to fight Samus at Frigate Orpheon. However, Samus knocks Mario away by firing upward with her Arm Cannon shortly after defeating Luigi.

Mario appears prominently in Ridley's reveal trailer, A Piercing Screech, where he and Mega Man accompany Samus on patrol of a mechanical area. However, Mario ends up ambushed by Ridley, who presumably crushes his head, leaving only his hat behind. Ridley is then seen twirling it on his finger. The manner in which Ridley killed Mario resembles a PTSD-induced hallucination by Samus in the Metroid manga, where Ridley was seen crushing the heads of Rodney and Virginia Aran, her parents, in a similar manner. On a similar note, the manner in which Ridley twirled his hat resembled Mario's actions in the teaser for Super Mario Odyssey.

The key art for the "Screw Up Your Opponents" tourney for Super Smash Bros. Ultimate features Mario as one of the characters utilizing the Screw Attack, a possible homage to Super Mario Bros. 3.

Trivia

 * If Mario gets a Starman in Super Mario Bros. 3 and subsequent remakes and games, he will be able to spin jump, and when he does, he will be covered in a sheath of rainbow energy. This bears strong resemblance to the Screw Attack.
 * Mario and Luigi: Partners in Time features an enemy similar to the Nightmare boss in Metroid Fusion called the Snoozorb. Similarities include both of their names pertaining to sleeping.