Regarding one of the Classics on eating placenta stew in this weeks Straight Dope email, Hugh Fearnley Whittingstall ate placenta during the making of his River Cottage TV series.
See one of the questions towards the bottom of this page
Cecil my have been a little off on how rare this is. I have a friend who is a midwife in the Chicago area (she will have to remain nameless due to the problems with being a practicing midwife in Illinois), but she always recommends her mothers to partake in eating the placenta in one way or another. They even (at times) make placenta butter (something akin to peanut or apple butter). Not only that, but I ran a video camera for her regional midwifery assocation, and it seemed to be par for the course among the several hundred midwives present. They even had a break out session on why it was good, different ways to prepare it, etc…
Personally, I’m not exactly comfortable with the thought, but they all seem to think it’s perfectly normal. I guess it all has to do with perspective…
Mmmmmmmm, placenta pâté. 
Just wanted to chime in that I used to be the one of my friends who could be counted on to make a joke about, um, “placentophagy” (is that a word?). Since this whole Tom Cruise thing came around, though, I’ve quit.
I know a couple who, following the birth of their child, took the placenta home and cooked it, but they were unable to bring themselves to eat it. They are vegetarians, so that probably didn’t exactly help set them up for it.
So if you eat placenta, does that make you a cannibal?
They threw out perfectly good food? Don’t they know there are starving doulas in China?
My perspective might be a bit off, considering where i live (yes, the San Francisco Bay Area really is a freak haven), but i also think Cecil’s estimation of the popularity might be a little low. I personally know at least four couples who have cooked and eaten placentas (placentae?) after their children were born. Granted, this is only anecdotal evidence, and i have no cite to back me up. It just seems odd that i would personally know so many if the practice is as rare as he alleges.