People insure some unlikely things.
Egon Ronay, the restaurant critic, insured his palate for £250,000 in 1993, arguing that without this asset he would be like a sculptor shorn of his hands.
While playing cricket for Australia between 1985 and 1994, fats bowler Merv Hughes took out an estimated $370,000 policy on his trademark walrus moustache, which, combined with his 6’4″ physique and outstanding playing ability, made him one of the most recognized cricketers in the world.

And in 2003 Basil Brush apparently insured his tail for £1M.
Boom! Boom!