Searching for a scientific explanation (i.e. an astronomical explanation) for the Star of Bethlehem would, to many skeptics, be putting the cart before the horse - it's much easier for people who do not believe the gospel narratives to say that the Star of Bethlehem was just a myth with no real basis in historical fact. That said, even many myths have bases in fact - and so people have attempted to come up with an astronomical explanation for the Star of Bethlehem beyond just that it was (or was not, as skeptics would say) a miraculous working of God.
According to the Christian tradition as recorded in the Gospel of Matthew, the Star of Bethlehem appeared in the skies to herald the birth of Christ, and several foreign Magi or "wise men" (given the context, one assumes astrologers) were guided by its light to Bethlehem, where they found Joseph, Mary, and the newborn Jesus. Early Christian theologians viewed this as a miraculous event and therefore saw no need to assign a naturalistic explanation to the event. After all, God could by definition do anything - including create lights in the sky without obvious reference to a natural cause.
After the Renaissance, however, astronomers began to attempt to provide a more detailed explanation. This was not, at least originally, entirely about disproving the gospel record by "proving" that the Magi had simply been fooled by an unusual star formation: many of that period believed that God had designed the universe to run mechanically, like clockwork, so that if strange lights appeared in the sky, God must have caused them to occur through some sort of natural process. Johannes Kepler, one of the early astronomers most responsible for the transition from geocentric to heliocentric conceptions of the universe, suggested that a conjunction between Jupiter and Saturn (which occurred several times in 7 B.C.) might have appeared as a new and exceptionally bright "star" in the sky. Subsequent analyses have predicted that, viewed from Earth, these planets would not have appeared in any real way out of the ordinary, however. Other planetary conjunctions are also a possibility.
Another explanation is that these early witnesses were seeing a comet. Halley's Comet past Earth in 12 B.C., and several years later, Korean and Chinese writings reveal that another comet or possibly a supernova (an exploding star) was also visible. A supernova occurring in distant Andromeda Galaxy might have been visible - but if it was, we have no real way of knowing today, because the remnants of such an explosion would not be visible at such a vast distance. Still, the phenomena described by the Asian astronomers in about 5 B.C. is close enough to the theoretical date of the birth of Christ ("0" A.D. is a medieval estimate which may be out by several years) that it could have been the same event.