XKCD wonders just what star, or planet, the wise men were following: 

There aren’t very many good astronomical candidates for the Star of Bethlehem (Chinese records don’t show a supernova at the right time, and none of the other obvious candidates check out) and, furthermore, there’s a lot of historical and theological debate over Jesus’s date of birth ("4 BC" seems to be the closest thing to a historical consensus date). These charts are all calculated for a somewhat arbitrary departure date from Jerusalem of December 25th, 1 AD; different departure days would lead to different paths, but the overall picture would be the same.