August 31, 1996
Some enemies in Crash Bandicoot are believed by some people to be refernces to the Mario series. Specifically the carnivorous plant enemies, called Venus Fly Trap, that look similar to Piranha Plants from Mario games, and turtle enemies that retreat in their shells once stomped on, similarly to Mario's Koopa Troopas. Unlike the Koopa Shells, though, the shell is not launched if Crash jumps on it, but instead works as a platform. Still unlike Koopas, these turtles slie on their back when retired in their shells, a trait more similar to Shellcreepers from Mario Bros.
Note that it's highly likely that these similarities are just coincidences due to the game's natural themes.
Crash Bandicoot 3: Warped
October 31, 1998
Baby T, found in the levels Dino Might! and Eggipus Rex, is an infant Tyrannosaurus Rex that Crash can ride and is believed by many to be based on Yoshi from the Mario series. Like Yoshi, he's found in an egg and runs away when he touches an enemy. Unlike Yoshi, tough, he cannot be chased back after running away. His appearance and the way Crash rides him are very similar to Yoshi.
Crash of the Titans
October 04, 2007
The Ratnicians can be heard sometimes saying "You thought he was an Italian plumber or something?" when they notice Crash.
Crash: Mind Over Mutant
October 07, 2008
The animated cutscene after defeating the brainwashed Crunch Bandicoot is named "Crunch Get!" in the cutscene viewer, likely after the phrase "Shine Get!" in the Japanese version of Super Mario Sunshine.
Crash Bandicoot's compay Sony didn't have any right over Nintendo's properties, but they only included minor references to the Mario series.