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 pair of shoes very similar to Sonic's can be seen next to a garbage can labeled "No hopers". This seems to imply that Sonic tried the challenge and failed, but since Nintendo had no right over Sega's character, we can only say that those shoes are similar to Sonic's, but aren't actually his.
In the Game Boy Advance version of the game, released in 2004, the garbage can was removed, probably because Nintendo's feud with Sega ended in 2002 with the closing of Sega's console-producing division.
Mario & Sonic at Beijing Olympics
November 06, 2007
Mario's biography for this game reads "This persistent little plumber developed his skills chasing down a big ape."
This is clearly a reference to the events from the original Donkey Kong.
Mario & Sonic at the Vancouver Olympics
October 13, 2009
Donkey Kong is a selectable character in Mario & Sonic at the Vancouver Olympics, as well as its sequels, but having already appeared in almost every sport game in the Mario series, he's considered to represent the Mario series, rather than his own (see here for informations about this appearance).
Nintendo had no right over Sonic in 1995, so they were only able to do a subtle reference.