An interesting question.
We know of more than 2,700.
If you take a look at the Alcohol and Tobacco Tax and Trade Bureau (TTB) listing of "wine producer and blender" permits, you'll find more than 3,850 entities who make wine (and act as control points for taxation) as of September, 2004.
As of February 2005, Wine Business Monthly (WBM) calculates that there are over 4,700 US wineries, based on those who hold TTB permits, and those who operate "virtually." Unfortunately, WBM doesn't provide a listing for us to see who they're counting.
Of course, we're most interested in wineries with Web sites. We'll keep you posted.