I am aware that an early draft of HTML5 specified peer-to-peer connections using the PeerToPeerConnection() constructor. However, this was replaced by WebSocket which, to my
It's not exactly P2P, but you can use proxy server using push mechanism
http://en.wikipedia.org/wiki/Push_technology
For example if you want to send data from Browser A to Browser B, you send that data to proxy server and that server push it to Browser B.
Opera Unite allows Peer to peer (basically gives your browser web server, file system and nat-traversal capabilities), but this is Opera only.