Already exists. It's just waiting for population http://www.i2p2.de/

It's strange that nobody already mentioned Tor and its hidden services:

https://www.torproject.org/docs/tor-hidden-service.html.en

I2P and Freenet aren't as widely used (AFAIK) and they are slower.

http://en.wikipedia.org/wiki/.onion

EDIT: There's also namecoin, that someone submitted:

http://news.ycombinator.com/item?id=2546815

And the MafiaaRedirector Firefox extension:

https://addons.mozilla.org/en-US/firefox/addon/mafiaafire-re...

http://freenetproject.org ? Also has the ability to run as a darknet, where only people you invite will even know the network exists.

Maybe we should start a darknet DNS service