I've yet to buy one, but from what I gather, they give a smoke similar to a Meerschaum in that there is no flavor imparted from the pipe. Also, the tip needs to be glazed or some other coating needs to be on the tip, otherwise your lips will stick to the pipe. Oh, and the bowl gets really hot. Again, this is what I've learned fro this site and a clay is on my short list of pipe purchases.
I posted elsewhere about these things on this forum. The old clay is a cultural thing - you either love them or loath the things. I am rather fond of them but the damage they do to your teeth made me get into amber stems as they are less abrasive.
I'll smoke a clay from time to time and find that they can be fine smokers but you do have to shop around to find quality ones. I've found that a lot of the white clays that you buy as "souvenirs" from historic places like Williamsburg are more suited for the tourist trade as a "souvenir" rather than a quality smoker. I have a reed stem clay pipe (sometimes referred to as a "trade pipe") that I smoke from time to time at Civil War reenactments. It's actually smokes well, although like many clay pipe bowls, it will start to get hot the longer you smoke it so you end up having to hold it near the base or by the stem close to the base. I haven't tried any of her pipes yet, but I'm intrigued with the historical clay pipes being made by Heather Coleman of DawnMist Studios in the UK. She is considered an expert on colonial clay pipes and has over 30 years of experience in collecting and researching clay pipes. She makes pipes as a sideline in runs so she doesn't always have a lot available for sale. Some of her pipes do have glazed ends whiles others do not (many colonial pipes from the late 16th through the 17th and 18th centuries would not have had glazed tips). I'm thinking about picking up a couple of her clays as well.
The only time I really reach for my clay is when I'm camping. I can smoke the thing a lot, not worry, and put it in the campfire coals to clean itself out.
Even then, a quality corn cob pipe is less prone to breakage. So, kind of just relegated to sitting around the campfire.
I've never really understood Arthur Conan Doyle's description of Sherlock Holmes' "oily black clay." I havn't ever seen one smoked to the point that it turned black or oily - not sure if that is possible - or if I havn't ever smoked mine enough.
Nowadays, the clay pipe is disappearing primarily for a few reasons:
They break easily, they get hot quickly, many can't pass a cleaner et. al.
However, of the clays I have, I find it useful to test new tobaccos instead of using a briar in my collection for fear of any dramatic ghosting. If you do end up getting a clay, be careful of the heat, and try and wet the stem portion with a bit of saliva so that it doesn't stick to your lips when you smoke a clay. Clays are cheap, and handy, and nostalgic.
I tried one of those "tavern" type clay pipes and thought it was trash. The 7" or so straight white clay pipes with about a 4 hit bowl on them. I then found out about these http://www.lepeltier-pipes.com/ and gave one a shot. It is still in my collection and gets smoked once a month or so. Lepeltier pipes deliver a good smoke. They are a bit more work to maintain or I would smoke it more. Sorta like the maintenance on a system pipe only a lot more area to deal with.