If you use a Hosted SharePoint 2010 and you try to open a Word Document or try to open a Document Library with Explorer SharePoint prompts for login credentials even you are already logged in. To stop this behavior in Internet Explorer you can simply add your SharePoint Site to the Local Intranet Zone.
This is because SharePoint uses Windows Authentication. We deiced to use Windows Authentication because only Windows Authentication allows you to easily use the full feature set of SharePoint Foundation 2010.
Open Internet options and click on the Security tab and choose Local Intranet
Now click on Sites. On the first Windows choose Advanced