"These strange-colored monsters or alebrijes were invented by Pedro Linares, who saw them in a dream when he was 30, and very sick.
While he lay in bed, unconscious, he dreamed of a strange and different place, rather like a forest with trees, animals, clouds, sky, rocks and other things, and where all the animals had turned into odd, unknown creatures.
He saw a donkey with butterfly wings, a rooster with an eagles head and others that all shouted the word, Alebrijes. The animals began to shout louder and louder, Alebrijes, Alebrijes, Alebrijes!
the sound was terrible and he wanted to get away. A man told him that it still wasn't time for him to be there and that he would have to start walking in order to find the exit. Later, he came across a narrow window, climbed through, and suddenly awoke.
When Pedro was able to get out of bed, he began to remember his dream and wanted his family and other people to see these animals. So, he took some paper and began to mold the figures he had seen; he then painted them like those he saw in his dream." - quote source
This online gallery titled "Beasts and Bones" has one of the better collections of Alebrije.
This flickr gallery has pictures from an Alebrije exhibit where they're shown on trophy mounts. They remind me of similar sculptures by Dr Seuss.
Wikipedia article on the Alebrije.
Here's a good article on the subject.
There's a few on display here.
And here's a few gigantic examples.
Many thanks to Kyuzalt for tipping me off to these fantastic sculptures.