According to the Internet Live Stats tracker the number of websites on the internet exceeds 1 billion-- a milestone figure reached on September 2014, if one in need of confirmation due to inactive website number fluctuations.
Internet Live States defines "website" as a unique hostname, a name one can resolve (via name server) into an IP address. Around 75% of websites are inactive, being parked domains and the like.
The figure follows the internet's 25th birthday on April this year. Back in 1989 Tim Berners-Lee invented the World Wide Web, together with the first web server, first browser, editor (the "WorldWideWeb.app") and HTTP. October 1990 saw the creation of the first version of HTML.
The first website (info.cern.ch) was published by Berners-Lee while at CERN on 6 August 1991. CERN made World Wide Web technology available for all on a royalty-free basis on 1993.
According to Internet Live Stats recent internet growth is tremendous-- during 2013 alone the web grew by over 30%, from around 630 million sites on January 2013 to over 850m by December 2013 (of which 150m are active).