There are many companies that operate using democracy as an organizing principle - Semco is the great-granddaddy of them all (two books - Maverick and the 7 Day Weekend - were written by Semco's founder, Ricardo Semler, about how Semco operates).
Other well-known democratically-run companies include Zappos, WL Gore, DaVita (a $12B company), and Dreamhost.
If you're interested, take a look at WorldBlu for more - they've been building a community of these kinds of companies, have tons of resources on their site, and even have a conference on organizational democracy.
 - http://www.amazon.com/The-Seven-Day-Weekend-Changing-Works/d...
 - http://www.amazon.com/books/dp/0446670553
 - http://worldblu.com/