I just came across a few interesting articles about cross-nursing (nursing other people's babies): "Breast Friends" and a response to the article: "She Breastfed My Son." I also found this British article called "Not Your Mother's Milk."
I've never thought it was weird, but I guess some people really freak out at the idea. My little sis in fact has a good friend due around the same time, and they've talked about nursing each others' babies if the need arises. For example, if they are watching each others' kids and the other baby becomes hungry, they will simply nurse the baby!
It's something I wouldn't do with a stranger or casual acquaintance, for health reasons. But with close friends or siblings, I wouldn't even blink if they asked me to. In fact I would be honored.
Donating breastmilk is similar, but since it's not given directly from the source, people don't have as much of the "yuck" reaction.
Would you do this for a friend or sibling? Would you mind if your friend nursed your own baby?