If there is any accuracy to data released by Netcraft, then the Internet has about 182,226,259 sites.  That's 948,000 more than a month ago.

Netcraft looks at the number of sites hosted on the different top servers. The following graph represents market share for top servers across all domains from August 1995 to October 2008:

Netcraft offers a more detailed look at the numbers of sites coming from different servers in this list. Amit Agarwal at Digital Inspiration compares NetCraft's data to that of another Firm:

Now Domain Tools also tracks all the different web domain names registered on the Internet and their count puts the total number of active domains as 106 million.