I never used to eat orange peels, but I've started doing it recently. In my efforts to lose weight, I thought that chewing on the orange peels would keep me from munching on other snack foods. The result is not a complete success, but it does seem to help.
Of course, I was a bit worried about how safe it was to eat the peel, but a Google search showed several sites indicating that they are safe to eat. Just be sure to wash them first so that there's no lingering wax or pesticides on the skin.
Now the taste of the orange peel isn't all that good, especially the white stuff, technically called the pith, is pretty bitter. You can get around this by eating the peel along with the fruit itself, or here's a site with a recipe for chocolate covered orange peel.
A big suprise for me was the possibility that eating the orange peel may be healthier than eating the actual fruit.