In some cases of users trying to open Word or other documents from a secured external SharePoint site, they are prompted for authentication to the site again as Word doesn't know they're already authenticated. If using Forms Authentication, this doesn't really work. There's an easy IE setting you can change that will have the document open in the browser, maintaining the authentication and not prompting the user again.
1. Click Start -> Programs -> Accessories -> Windows Explorer (not IE, but Windows Explorer).
2. On the menu, click Tools -> Folder Options.
3. Go to the File Types tab.
4. Scroll down and select the DOC extension (Or xls or what ever you're changing it for).
5. Click the Advanced button.
6. Select the "Browse in same window" option and click OK twice.
Now when the user clicks to open the document, it will load in word inside the browser window without an additional prompt for authentication.