Donkey Kong is an arcade game released by Nintendo in 1981. This is where Miyamoto began hitting it out of the park, causing quarter shortages in arcades the world over. The game is a far cry from more modern titles, but was revolutionary for the time.
According to Wikipedia, "In the game, Mario (originally named Mr. Video and then Jumpman)must rescue a damsel in distress named Pauline
(originally named Lady), from a giant ape named Donkey Kong. The hero and ape later became two of Nintendo's most popular and recognizable characters. Donkey Kong is one of the most important titles from the Golden Age of Video Arcade Games, and is one of the most popular arcade games of all time."
The Original Arcade version of Donkey Kong.
Donkey Kong in his Original form. Miyamoto is credited with his creation also.
Donkey Kong & his sidekick Diddy Kong as they appear in the current generation.
"Released in 1994, Donkey Kong Country (in Japan, Super Donkey Kong) was an entirely new DK series established by the British company Rare and Tim Stamper which took the Donkey Kong premise in an entirely new direction and became a showcase title to show off then-revolutionary CGI graphics. In Donkey Kong Country, the original Donkey Kong's grandson, also called Donkey Kong, was the hero and he and his sidekick Diddy Kong had to save his hoard of bananas from the thieving King K. Rool and his Kremling Krew. The game was an action sidescrolling title similar to the Mario games and was enormously popular for its graphics, music and gameplay." - Wikipedia
A screenshot from one of the newest Donkey Kong Country games, Donkey Kong Country Returns.