Trivial science fact of the day: Diamonds, particularly high quality ones, are very pure carbon (C). Sometimes small amounts of Boron (B) or Nitrogen (N) are found in diamond. These are carbon's neighbours in the periodic table and they give diamonds different colours.
So… despite consisting of pure carbon (an element), diamond isn’t an element because, in order to be a diamond, the carbon atoms must be bonded to their neighbours in a specific cubic arrangement. Neither is diamond a compound, because a compound is made up of two or more elements within each of its molecules.
EDIT: Just elaborating on "Diamonds are minerals," in case anyone is interested. ;-)