If your sharepoint site is in your trusted sites and is set to use existing user and password for authentication, but it still prompts for authentication, there is a fix. You may find when prompted for authentication that you can click cancel on the prompt and the Office document will open. If you want to do away with the prompt for authentication try this regedit.
1) Run regedit
2) Browse to: HKLM\System\CurrentControlSet\services\WebClient\Parameters
3) Create a new Multi-String Value called ‘AuthForwardServerList’
4) Enter each web address as a value of the 'AuthForwardServerList'
a. Do not include port numbers
5) Reboot the computer
6) The documents should now open without being prompted for authentication.