Mundo is the Spanish, Filipino, and Portuguese word for "world".
The icons for Dr. Mundo's Burning AgonyBurning Agony and Masochism skills used in game on the champion info screen show him in his original model, which was used in the early closed beta. In fact, we can see that model on a coffin of Voodoo Shaman in Autumn version of Summoner's Rift.
Dr. Mundo's quote "Mundo...mmm...*slurp*...smash!" may be a reference to the Hulk, a Marvel Comics character.
Dr. Mundo's famous quote, "Mundo will go where he pleases." may be a reference to Duke Nukem's quote, "I'll go where I please, and please where I go." This quote is also popular in the League of Legends community.
For Dr. Mundo's Corporate skin, many of the quotes are references from various office comedies, such as from the movie Office Space.