The condition these goats have is myotonia congentia and as a result they are often called Myotonic goats, fainting goats, or wooden leg goats. The gene responsible for this condition is recessive, but has been found in other animals, including humans and cats.
I found the above video on YouTube, it is not my Goat, his name is Gonzo.
In the goats one sudden scare causes their muscles to freeze up, they lose balance and fall to their side. The younger goats are more prone to falling, as the older ones soon learn to brace themselves. Although once used as meat goats these animals have since become popular as novelty pets.
Myotonic goats tend to be docile as a result of their condition and have a poor time climbing fences - which is something many other goats are noted for doing, as such they can be good pets for people who are new to the world of keeping goats. The biggest concern is that they are very vulnerable to predators, such as coyotes or dogs. It is not necessarily true that predators will be confused when the goat falls over, it might just be thrilled at the chance for an easier kill.
If you are looking for a cute, novelty, goat breed, then Myotonic goats may be just what you are looking for. I have seen prices at the Innisfail Auction Market, Alberta, for Myotonic goats being anywhere from $30 to over $100.