This question is impossible to answer with any accuracy since no one is in charge of the World Wide Web and there is not one central "server" that runs all the websites in the world. The DNS registrars have lists of the domain names that exist, but not every domain contains a website, many domains contain more than one, and the registrars are not under any obligation to tell the rest of us exactly how many domains their databases contain.

However, many people have tried to estimate the size of the Internet. One thing we can be sure of is that its growing, rapidly.

At the turn of the last decade, researchers at the Online Computer Library Center, conducted a survey and concluded that the Web contained some 7 million unique sites. This was a 50% increase compared to 4.7 million for 1999.
In another survey in November 2006, responses were received from 101,435,253 sites. This easily beating the previous record of 17. The Internet doubled in side between since May 2004 and November 2008
.
Nost sources:
http://news.netcraft.com/archives/2006/11/01/november_2006_web_server_survey.htm...
http://www.boutell.com/newfaq/misc/sizeofweb.html

There is no exact way to know as there are so many differentials to ever find out precisely.

Netcraft Web Server Survey found 108,810,358 distinct websites.

Of course, Netcraft's survey isn't perfect - there may be websites in the world that were not discovered by Netcraft's software. So, as of this writing, "there are more than 108 million websites" is the most accurate statement that can be made.

http://www.boutell.com/newfaq/misc/sizeofweb.html