How many active Bitcoin nodes are there?

[Shatosi Makanoto]

Is there any way to know or estimate how many nodes are active on the network? I'm concerned because it seems as though the interconnection of nodes is quite random, and so the number of hops required for data to be distributed around the network could be very high. The problem is mitigated by the fact that there are super-nodes that have tens of thousands of connections (https://blockchain.info/hub-nodes), but that introduces another problem: single points of failure or government interference.