In a lot of ways, it was Donkey Kong that made Nintendo. Of course it was Super Mario Brothers which was responsible for the domination of the NES/ Famicom in the 80s, making Nintendo a household name. But it was Donkey Kong which not only made Nintendo into a presence in the global video game market, but is also responsible for video games as we know them today.
Nintendo games were a big hit in Japanese arcades, but were a bit of a flop when the company tried to expand to the US. Donkey Kong was designed specifically to appeal to US markets, and seems to have been successful at doing so, making Nintendo a contender in the global market.
Donkey Kong was the first multi-level platform game, as well as the first video game to include a backstory and cutscenes. Also, Donkey Kong is responsible for the creation of Mario, named for the cranky landlord who owned Nintendo of America headquarters, who has grown to be nearly as iconic as Mickey Mouse. Without the advent of Mario, there would have been no Super Mario Brothers to lead Nintendo to become "the" name for consul video games after the video game crash of 1983.