Nope, it doesn't matter at all. Many sites have stopped using the www in their URL.
The only issue that used to be around is if your site responded to both the www version and the non www version. Then, if people linked to both it would sometimes czuse duplicate content issues with search engines. I don't think this is as much of a problem these days, but to prevent it, many webmasters use an .htaccess file to make sure the site works both ways, but only shows up one way consistently.