I definitely wouldn't eat placenta, but there is some evidence that it could be beneficial. It supposedly reduces the risk of postpartum depression, and is apparently good in the case of postpartum hemmorage.
I heard a story from a midwife who had a client who had some hemmoraging after a homebirth. The woman didn't want to transport unless it was absolutely necessary. She was very pale and feeling faint, so as a last resort they "whipped up a placenta smoothy". Within 5 mintues, the woman was feeling much better, and they didn't need to transport.
I had always thought that the placenta had to be raw for full effect though. I think cooking would reduce a lot of the nutrients. Some women freeze-dry the placenta, and get it put into capsules.
Burying the placenta and planting a tree or something over top is pretty common after a homebirth, as midwives usually aren't allowed to transport it to hospital for incineration.
I definitely couldn't bring myself to cook up a placenta and eat it! A wee bit icky.