These are Tennessee Fainting Goats. Not a very good picture I am afraid but the location wasn't conducive to taking photos (taken in Calistoga, California, on our USA trip in 2008).
The following information from Wikipedia explains about their fainting episodes:
"A fainting goat is a breed of domestic goat whose muscles freeze for roughly 10 seconds when the goat is startled. Though painless, this generally results in the animal collapsing on its side. The characteristic is caused by a hereditary genetic disorder called myotonia congenita. When startled, younger goats will stiffen and fall over. Older goats learn to spread their legs or lean against something when startled, and often they continue to run about in an awkward, stiff-legged shuffle."