OK, so "hosted" doesn't mean a web-based interface using a browser. It means that someone, somewhere stores your data on their server. They are responsible for backups and updating the software with new releases.

Most of the companies doing that are using Terminal Services or Citrix. Sage is a prominent example in this market. You access their server using your web-browser but once on their server, the screen interface is exactly the same as if it was on your desktop.

I acknowledge the benefits of someone else doing the IT work for you. However on the other side of the ledger, your data resides somewhere else.

• What if the host goes out of business?
  
• Can you trust that your data is secure and private at all times?
  
• What if you want to add a 3rd-party application (i.e. payroll)?
  
• What if you want to get a copy of your data? How would you do that?
  
• How difficult is it to get the host to restore last night's backup?
  
• What if, as Andrew pointed out, access to their site goes down for a number of hours?
  
• What is the monthly cost for this (in)convenience?
  

I would still recommend Terminal Services. It's less expensive, your data is local & private, performance is good, maintenance is centralized to one computer/server and you're in control. Plus you can get access from remote locations (like a cafe in Europe)!