August 31, 1996
The Toxic Waste level in Crash Bandicoot consists mainly in jumping over barrels, and it may be a homage to the 25m level from Donkey Kong. By extension the Barrel Thrower enemy, only found in this level, may be a homage to Donkey Kong himself.
Crash Bandicoot 2: Cortex Strikes Back
October 10, 1997
In some ruin levels, there is a gorilla enemy who attacks by throwing logs at Crash, and therefore might be a parody of Donkey Kong.
Additionally in mountain levels there's a "lab assistant" enemy who attacks using a big hammer and wears blue overalls over a red shirt, and a red cap on his head, and therefore might be a parody of Mario.
Crash Bandicoot: The Wrath of Cortex
October 27, 2001
An area in the level "Crash and Burn" consists of some sloping platforms with rocks rolling down them that have to be jumped over. It resembles the 25m level from Donkey Kong, and might be based on it, but it may just be a coincidence.
August 30, 2004
An area in the level "High Sea Hi-Jinks" features some slopes with a rhino enemy on top throwing barrels. This might be based on the 25m level from Donkey Kong.
Crash Bandicoot's compay Sony didn't have any right over Nintendo's properties, but they only included minor references to Donkey Kong.