HAHAHA, that is almost unanswerable. There are billions of websites out there. Even just main pages. Maybe trillions. And with new sites coming on every second of the day(literally) there are as many being removed from the internet as well. The internet is just thousands of servers, computer, cables, boosters, radio waves. The internet is "the biggest network in the world" with 6 billion people on the planet, it is vitually impossible to keep a count!!!
According to Google.com and Boutell.com (as of Spring 2004) there were approximately 43 million web sites.
Paul Metheney, metheney.com
If you look at the bottom of the Google screen, you'll see that Google catalogs over 8 billion websites. I have no idea how many there are that they do not catalog.