I heard at a lecture last night that the word Palestine comes from the Roman word for Philistines, but I remember once reading that it came from the ancient deity Pales. What's the real story?
It's from a Greek transliteration of Pelesheth (transliterated in the KJV as Philistia) "land of the Philistines." Herodotus rendered this as Palaistine and after the Bar Kochba revolt, the Romans called the region Syria Palaestina or just plain Palaestina as a way to remove any Jewish association from the name.
In addition to /u/brojangles comment it's worth noting that the Arabic for Palestine is فلسطين, pronounced pretty much identically to "Philistine".