Depending upon the level of support that you require, you can even purchase 24/7 support ($50 per year, per user) and extended business hour phone support as well. While Google is not really competing with Microsoft Office, this product is seen by many as a nice supplement, especially for small businesses that may not require everyone to have an email client.
To answer your question directly, yes, organizations have been using Gmail for business. Is it the right solution for your organization? I can't make that decision for you. Why not test it out in a lab with a pilot of users, taking advantage of the free trial offered by Google. Understand that Google apps (with Gmail) are not mature products like Office, and while they has incredible potential, no one is suggesting at this time that they will replace Microsoft's offerings anytime soon.
This was first published in September 2007