Clay pipes were thought to have first been smoked in Englad in the 16th century. This was about the time that Sir Walter Raleigh promoted smoking of tobacco from the "New World" in pipes. Clay pipes fell out of common usage most recently in the 1930's when changes in society (primarily the introduction of pre-made cigarettes) relegated the clay pipes to novelty status.
Clay pipes of any quality are hand-made using the technique shown below. Clay pipes tend to burn hotter than other types of tobacco pipes and can be a challenge for most pipe smokers. Fans of clay pipes claim that unlike briar and corncobs their favorite pipe material gives a cleaner smoke where the pipe medium doesn't intrude on the taste of the tobacco. Cleaning a clay pipe takes a special hand because the draft hole on almost all clay pipes is too small to run a pipe cleaner through. As such, care must be taken to not allow the pipes to clog. They are also fairly fragile and can be easily broken.
Here is a video by Radio Batavia that demonstrates the making of Clay Pipes at the municipal museum in Gouda, Holland.