Mr. Chunks

Mr. Chunks is a two-headed alien goat. One head constantly pukes and the other constantly excretes diarrhea. Fry and Bender used Mr. Chunks to fill up a pool with his "leavings", so that the one with the less Twitcher followers had to jump in it. (The winner's grande prize would be a buck.) There was a tie but, even so, Fry jumped in, recorded the video and uploaded it to Twitcher to stop people from laughing at Leela. The goat later died.

Friends
He was possibly a mascot of Planet Express, although this is never mentioned in "Attack of the Killer App". Mr. Chunks was familiar to Amy and Bender, and very dear to Fry, who cried after the goat's death. It's unknown if he was close to the Professor even if the Professor knew about him. Also, Leela didn't seem to care much.

Trivia

 * is an actual condition on humans, but it's more commonly noted on other animals. Multi-headed animals are often depicted in mythology as supernatural and mystical. This is possibly why most people don't believe in their existence.
 * Fry refers to Mr. Chunks as a puke-me-poop-ewe, possibly its species name, but in any event, a play on the two-headed creature, the pushmi-pullyu, from the classic children’s series.