Peacock tail spots are called eyes.

Eyes

Well of the 4 incorrect answers here, you combine a word mentioned by some of them (both words mentioned by asmita) with the word you used and get - eyespots ! Confirmation, in case you think I am being facetious; second paragraph, at bottom http://en.wikipedia.org/wiki/Eyespot_(mi...

Also, if you want to be fancy, oculus, Latin for eye.

They are called eyes.