Long ago, on the steppes to the east, were tribes of horsemen who put down their bows when they first learned magic. As mounted spellcasters, they managed to conquer and control a great empire for a few centuries using only a few spells well-learned. Whether they angered the wrong wizard or accidentally unleashed a wave of chaos through their use of magic is up to you.
The descendants of this tribe of mounted mages come in several forms:
Horse-heads are intelligent beings with human bodies and horse heads. They are carnivorous and will eat other forms of centaur (or their own in certain situations). They are chaotic and will do anything they can to make humans and other centaurs suffer. They cannot breed among themselves, so they capture breeding stock of humanoids and centaurs.
Two-face centaurs have human torsos embedded somewhere in or on the body of a horse, often in very inconvenient positons. The horse head is also present and has the intelligence of a normal horse. Patterns of control over the body vary and in general it is a struggle.
Cloppers are similar to fauns in satyrs in form. They have human upper halves and horse lower halves, which are smaller and slimmer than the hindquarters of a horse.
Centaurs are largely subject to the drives of their equine halves, so it is not unusual for combinations of the above to exist: cloppers with horse heads, horse-heads with a human face stretched over horse skull, even three-face centaurs might be found.
Those surviving centaurs created by the original event change form between these uncontrollably, or are in even more disturbing shapes. There is a unique centaur that is the torse of a man attached to a small herd of headless horse bodies which are connected by various tendrils extending between bodies.