I think the idea has a promising future. Google Docs & Spreadsheets has completely changed the way I, and many academic physicians I know, write abstracts and articles. I rarely use MS Word anymore -- Google Docs is just so much more convenient.
Of course, the Fortune 500 companies and many hospitals feel nervous about outsourcing their IT departments. They would like to protect their valuable company information which is understandable. HIPAA issues aside though, we may by surprised by how shortsighted this thinking is. Not outsourcing your files to Google (or other Internet giant), may one day feel just as weird as running your own phone company in order not to outsource your phone calls.
SF Bay Pediatrics, a medical group in San Francisco uses Google Apps and their Chief Information Officer recorded a video testimonial:
"When it comes to our email systems, our doctors don't have the time or the budgets to deal with managing technology or defending against spam. With Google Apps we don't have to worry about downloading the latest spam filters or navigating unwieldy servers – this is where we let Google do what it does best, so we can do what we do best – help our patients."