Hamachi is a UDP-based virtual private networking system. Its peers utilize the help of a 3rd node called mediation server to locate each other and to boot strap the connection between themselves. The connection itself is direct and once it's established no traffic flows through our servers.
Hamachi is not just truly peer-to-peer, it is verifiably secure peer-to-peer.
Believe it or not, but we are able to successfully mediate p2p connections in roughly 97% of all cases we dealt with so far (few tens of thousands as of early March). This includes peers sitting behind different firewalls and/or broadband routers (aka NAT devices).