For various reasons, this has been in the news again recently. The idea is that everyone is connected to everyone else by, on average, 6 links. There is some debate that this is just an academic urban myth though, but it is an idea that captures the imagination.
Someone even tried an experiment on facebook to see if they could get everyone on facebook to sign up to a group just from receiving invites from friends (so not necessarily proving 6-degrees, but showing that everyone is actually connected via a friend-of-a-friend-of-a-friend).
Whether its true or not, its all fascinating stuff and many people have had a tinker with the idea.