There is some wonderful information about building healthy placentas in Nina Planck's new book, Real Food for Mother and Baby: The Fertility Diet, Eating for Two, and Baby's First Foods.
As for me, I froze my placenta in a round plastic take-out container and 7 months later carried it onto a cross country flight in a cooler. My husband and I then thawed and buried it in one of my families most magical places. Fortunately it is a place that will always be in my family, so I feel great about the placenta nourishing the earth there. We then planted a flowering plant over it and now we visit it every year.
It is a wonderful reminder of the joy of giving birth. :)
I have a story. My third baby was born at home in March, 11 days late. My sister in law overheard the midwives talking in the kitchen after the birth, saying how horrible the placenta looked. They thought it had all come out of me, but apparently there were a lot of thick calcium deposits all over it and one of the midwives said she'd never seen anything like it! Yikes. A few days later I started feeling very bad - fever, chills, malaise, and eventually - TMI warning ***************** I passed several chunks of rotten placenta at 3, 4 and 5 days postpartum that I had retained. I had to go on antibiotics and methergine. I have attatched a picture of the aforementioned placenta for your viewing pleasure. :) We threw it away. We've always rented whenever I've given birth, so we haven't planted any trees in the yard or anything.