If a Windows 7 computer using IE 9 (or 8) is prompted for a username and password when accessing Word or Excel documents on SharePoint there are some things that can be done.
First, make sure the site is in the local intranet zone and that "Automatic Logon only in Intranet Zone" is selected in Internet Options. To verify this setting, close all IE windows and Office apps connected to the sharepoint server. Then in Control Panel open up Credential Manager and remove any credentials to the server (run "control userpasswords2" in Vista). If you're logged into your computer using a domain account, then the next time you open the SharePoint page it should automatically log in.
If the connection to the server is using a Fully Qualified Domain Name (FQDN), there are some additional steps that may need to be completed so Office doesn't prompt for a username. The notes below are sourced to MS article http://support.microsoft.com/kb/943280:
In the registry, browse to HKLM\System\CCS\Services\WebClient\Parameters and add a multi-string value named "AuthForwardServerList" (without quotes). Then add *.domain.com as a value.
These two settings have fixed almost all credential problems in both Vista and 7. I still have some lingering XP machines that are dealing with credential prompts... if I find an answer I'll post it.
