They are apparently the only part our current cats do not like. Khannie used to bite off the heads and leave the poor headless body on display. And once, the only part I found was a stomach with a small bit of intestine attached (Zoo 101 FTW!).
My sister's cat would catch mice and eat everything but the tail. That was left on the back doorstep as a trophy (I guess). Mother was not amused.