Sega
Sega is the rival company of Nintendo. The mascot of Sega is Sonic the Hedgehog. Both companies have been making fun of their mascots-Sega has made fun of Mario and Mario games have made fun of Sonic.
In the back of the box of Sonic the Hedgehog includes "Super", a mockery of Super Mario Bros.. Also in Sonic the Comic (British comic) a reference to the Mario Bros. is made. There are characters called the "Marxio Brothers".
Sonic made a "cameo apperance" in Donkey Kong Country 2. Thought he joined Cranky Kong's contest of collecting DK Coins, Sonic did not suceed and did not get many coins. Sonic did not even rank third place, and angryly ran away from the Mushroom Planet. Sonic left his shoes behind when he left. In the game, the player can only see Sonic's shoes and the game doesn't tell any story of Sonic failing or running away. This was a Sonic mockery made by Nintendo.
Also Harry Hedgehogs from Super Mario World 2: Yoshi's Island may be a mockery of Sonic the Hedgehog.
Team Up
Thought these companies are rivals, Nintendo and Sega actually teamed up to create a crossover game featuring Mario and Sonic. Sega and Nintendo are both working on Mario & Sonic at the Olympic Games and many fans were amazed that two rival companies teamed up.