This is one of those things that I can’t believe I’d never heard of before. A mainstream cartoon made over 70 years ago that tells the story of a group of animals living in the post-apocalyptic ruins of Man’s never ending wars.
I was browsing the forums on PAMedia.com today and came across a thread about the cartoon, released in 1939, called Peace on Earth.  It runs about eight and a half minutes, and has Grandpa Squirrel trying to explain to his grandchildren what “Man” was and how they killed themselves off.
The cartoon itself is great.  The animation is fantastic, and through flashbacks we see battle after battle until the final two men alive face off against each other.  The animals then discover the ruins of a destroyed church, and decide to start a society based on peace to avoid Man’s fate.
Then, to make the fact that I’d never came across it before even worse, I found that cartoon was remade in 1955, by none other than Hanna Barbera, and that version is even better.  A lot of the remake is identical to the original, including some scenes and dialog, but in the pre-WWII version, Man kills himself off through conventional war.  In the newer version, the cause of the his extinction is nuclear weapons.
I would say both should be rated as “must see” for any fan of the post-apocalyptic genre, particularly if you’re interested in historic examples, as I am.  So, both are presented below.

Peace On Earth (1939) – Classic MGM Cartoon from megarachnid on Vimeo.