When I think of these creatures I always think of the Film and Book, The Lion, The Witch And The Wardrobe. Centaur's are half human, half horse - the upper half of their body being human and the lower half being horse. They are born from the God Apollo and Stilbe, daughter of the river God Peneus. Other tales have them as offspring of others, notably the Magnesian mares and Apollo, or sometimes Centaurus.
Despite Apollo being the father of the Centaurs, these creatures actually followed Dionysus, the wine God. They were described as being wild in nature and untamed, they excelled at archery and were fond of wines and grapes. However, they were reported to have gotten drunk really easily and would rape young maidens and trample over the crops of farmers. They were said to be ruled by their wild instincts and untamed nature.
Perhaps the best known tale of the Centaurs is where they showed up at the wedding of Pirithous, king of the Lapiths. They became drunk on the wine that was offered and got into a quarrel, which in turn led to a huge fight. The Centaurs ravaged the wedding, attempted to kill Hercules who was a guest at the wedding. They ravaged the bridesmaids and stole the bride. This resulted in a huge battle that saw them being driven out of Thessaly, with only the wise and gentle Centaur, Chiron, remaining.
The image that I have of the gentle Centaurs - such as in the Lion, Witch, Wardrobe - is a lot different to how they are portrayed throughout history.