A peculiar feature of the Amu Darya is the fact that all of its water did not always flow into the Aral Sea. At certain periods one branch swerved, shortly after having reached the apex of the delta, northwest and then southwest, passing by medieval Urgench. Called Uzboy, this branch then pursued the southwesterly course all the way to the Caspian Sea, which it entered through a wide coastal plain south of Krasnovodsk (Turkmenbashy)...In 1576 the river swerved back toward the Aral Sea, and the definitive decline of Old Urgench, thus deprived of its water supply, is by some historians attributed more to this natural cause than to devastations wrought by the armies of Genghis Khan and Timur.
This interesting little book first published over 100 years ago studies the old course. The Syr Darya has also had a changing course over the years.
This site details the changes well. It appears that irrigation played a part in the course change: "Jenkinson, the envoy of Queen Elizabeth, wrote in 1558-59 describing how the Oxus ran in the Uzboi channel but no longer reached the Caspian Sea, and predicting that the demands for irrigation would soon lead to a complete desolation of the region. "
From 1221 to 1576ish the Amu Darya flowed into both seas. There was a change in the river in 1221 because the Mongols destroyed a dam on the river. At different times before then, the water flowed into both seas, or just the Aral Sea. Finally, the Seleucides considered building a canal between the Caspian and Black Seas so that merchandise could be transported up the Amu Darya (which was obviously flowing into the Caspian at the time), across the Caspian and through the canal to the Black Sea. It's amazing to think of shipping going on across those areas!
UNESCO has some maps of the previous forms of the Aral Sea. These maps are very interesting and if you don't click on anything else in this post, check out these maps. Archaeologists have been able to learn more about some of the earliest towns near the Aral that were later flooded (search for Aral).
You might think I'm odd, but I think this is fascinating, especially to see how both artificial and natural changes have had such an effect on this little lake. I love it when history, science, and geography come together.