Three that we know of:
Unicorn hair - a common core for wands; it's one of the three that Ollivander uses (the other two are dragon heartstring and phoenix feather).
Veela hair - the only person we know of with a Veela-hair wand is Fleur Delacour. She said the hair belonged to her grandmother, who was a full-blooded Veela (making Fleur herself one-quarter Veela).
Thestral hair - the core of the Elder Wand is a thestral hair.