Original Skype was mine blowing at the time because it was able to send files peer to peer even when people were behind firewalls. Peer to peer file transfers were the norm at the time, but when both parties were behind firewall file transfers wouldn't work, obviously. Skype used different hacks like UDP punch to establish P2P connection and if everything failed then it would fall back to proxying.
Skype was wild with how aggressively it tried to create a direct connection. I love it for its tenacity but it would do things like open up listening sockets on common server ports (so it would conflict with e.g. a webserver) which drove me nuts at the time