My have things changed. The number is probably in the millions to tens of millions considering people often set up networks at home.

RFC 1118 – Hitchhikers guide to the Internet. E. Krol.

When the Internet was designed it was to have about 50 connected networks. With the explosion of networking, the number is now approaching 1000. The software in a group of critical gateways (called the core gateways) are not able to pass or store much more than that number. In the short term, core reallocation and recoding has raised the number slightly.