There is a famous passage in Herodotus which is often brought up when questions of his 'believability' come up. From book II (Gutenberg text):

75. There is a region moreover in Arabia, situated nearly over against the city of Buto, to which place I came to inquire about the winged serpents: and when I came thither I saw bones of serpents and spines in quantity so great that it is impossible to make report of the number, and there were heaps of spines, some heaps large and others less large and others smaller still than these, and these heaps were many in number. This region in which the spines are scattered upon the ground is of the nature of an entrance from a narrow mountain pass to a great plain, which plain adjoins the plain of Egypt; and the story goes that at the beginning of spring winged serpents from Arabia fly towards Egypt, and the birds called ibises meet them at the entrance to this country and do not suffer the serpents to go by but kill them. On account of this deed it is (say the Arabians) that the ibis has come to be greatly honoured by the Egyptians, and the Egyptians also agree that it is for this reason that they honour these birds. 76. The outward form of the ibis is this:--it is a deep black all over, and has legs like those of a crane and a very curved beak, and in size it is about equal to a rail: this is the appearance of the black kind which fight with the serpents, but of those which most crowd round men's feet (for there are two several kinds of ibises) the head is bare and also the whole of the throat, and it is white in feathering except the head and neck and the extremities of the wings and the rump (in all these parts of which I have spoken it is a deep black), while in legs and in the form of the head it resembles the other. As for the serpent its form is like that of the watersnake; and it has wings not feathered but most nearly resembling the wings of the bat. Let so much suffice as has been said now concerning sacred animals.

Here's an excerpt from something in Science Daily:

During his first study, published in Nature in August 2002, Socha described a few aerodynamic features of the paradise tree snake -- one of five snake species that are purported to "fly." He videotaped and photographed various snakes taking off from a 33-foot-high tower in an open field at the Singapore Zoological Gardens. He positioned two video cameras to record in stereo, enabling the 3-D reconstruction of the head, midpoint and vent coordinates of the snake throughout its trajectory.

Socha found that the snake uses its ribs to change its body shape; it flattens from head to vent. The snake takes control of its flight by undulating through the air in a distinctive S-shape as if swimming -- moving the tail up and down and side-to-side. While gliding, these snakes make turns up to 90 degrees and always seemed to land without injury.

... if you read the rest of the article, you find that the snakes live in southeast Asia ... still, it's one of those things that makes you go hmmmmmmmmmmm