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:

1. Copy the URL of the Document Library to the clipboard
2. Open Windows Explorer
3. Right-click "Network" and click "Map Network Drive" to display the dialog "Map Network Drive"
   
4. In the dialog click "Connect to a Web site that you can use to store your documents and pictures" to display the dialog "Add Network Location"
5. In the dialog click "Next" and then "Next" again to display a new dialog
6. In the textbox "Internet or network address" paste the copied URL of the Document Library
7. Delete the "https:" part of the URL
8. Replace every forward slash with a backward slash
9. Insert "@ssl" after ".com"
10. Finish the dialogs

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.

1. Open the document library in SharePoint Online
2. Copy the URL of the document library to the Clipboard (e.g https://mso365wiz.sharepoint.com/Docs/Forms/AllItems.aspx)
3. Open a new Word document
4. Click Save As to open the Save As dialog
5. Paste the URL from the clipboard into the Address text box at the top of the Save As dialog
6. Delete /Forms/AllItems.aspx from the URL in the text box
7. Press Enter to open the document library
8. Right-click Favorites (top left of the Save As dialog)
9. Click Add current location to Favorites
10. Rename the new shortcut (optional)