Earthworm Jim: Special Edition
March 15, 1995
This game features several secret masks for the main character, including one of Donkey Kong with an arrow through his head. This is supposedly to spite Nintendo as the release of Donkey Kong Country around the same time prevented Earthworm Jim from making more of an impact.
To unlock the mask pause the game and press: Down + C, B, A, A, A, A, B, C
Donkey Kong Country 2: Diddy's Kong Quest
November 20, 1995
In Cranky Kong's video game hero challenge, while the first three places are taken by famous Nintendo heroes (Mario, Yoshi and Link), in the bottom right corner a gun very similar to Earthworm Jim's can be seen next to a garbage can labeled "No hopers". This seems to imply that Jim tried the challenge and failed, but since Nintendo had no right over Shiny Entertainment's character we can only say that that gun is similar to Jim's, but isn't actually his.
In the Game Boy Advance version of the game, released in 2004, the garbage can was removed, possibly because of the lack of the Earthworm Jim's popularity in these years.
The two series' companies had no right over the other one, so they were only able to do subtle references to each other.