While Americans debate the proper length of a lamb's tail, in other countries they eat docked tails. Apparently, they eat them in New Zealand, or at least they used to.
If this interests or intrigues you, check out this blog entry. The author equates eating lamb tails with eating ribs. There's also a Kiwi recipe for lamb tail curry soup and fried mountain oysters (lamb testicles).
In the Middle East, it's far more traditional to eat or cook with sheep-tail fat. Fat-tailed sheep, which comprise 25 percent of the world's sheep population, concentrate their fat in their tail and rump region. The only fat-tailed sheep in the U.S. is the Karakul.
Sheep-tail fat is called allyah (in Arabic). Though other fats and oils have largely replaced sheep-tail fat, it is still used in modern Arabic cookery, especially in rural, mountaineous areas. You'll find lots of recipes on the Internet that call for sheep-tail fat.
Historical religious text (Hadith) claims that sheep-tail fat was a "cure" for sciatica (lower back and leg pain caused by irriation of the sciatic nerve).