Is it possible to share your iTunes wish list with your friends?
Not to the best of my knowledge, no.
If the possibility doesn't exist, isn't it a great idea to add it?
Seems like a useful idea. You can suggest it to Apple here:
http://www.apple.com/feedback/itunesapp.html
What else would you do with a wish list than send it to someone who would like to buy you gifts?
The Wish List is basically an altered version of the old Shopping Cart and was developed for people who wanted a way to hold items for possible later purchase. I agree that it seems rather weak - a true, Amazon-style Wish List that you could share with others, along with the old Shopping Cart, would be more useful, I think. Perhaps if enough people request it, Apple will make it a priority for a future update.