I often get asked if its possible to map a SharePoint Online Document Library in Windows Explorer e.g. for easy opening of files a.s.o directly from Windows Explorer.
It is certainly possible:
Create a Document Library - in this example called "DocRepository". Since the name of my Office 365 tenant in this example is "mso365wiz" the URL to the Document Library is "https://mso365wiz.sharepoint.com/DocRepository"
In order to map the files in this Document Library in Windows Explorer the trick is to:
In my example the URL is "https://mso365wiz.sharepoint.com/DocRepository" and should hence be "\\mso365wiz.sharepoint.com@ssl\DocRepository" after the above changes.
You should now be able to access the Document Library from your Windows Explorer.
See also this support article
Update (February 2012):
SharePoint Online in Office 365 uses forms based authentication and the user is authenticated using a SAML token. This SAML token expires every 2 hours (some say longer though). After that the mapped drive for the SharePoint library cant access the library unless the user signs in to the SharePoint Online site again from the browser, even if the user tick off "Keep me signed in". As an alternative you can add the URL of the document library to Favorites in Windows Explorer. You'll need to do that via e.g. Word.