Probably most of us have experienced this! Very annoying!
The solution is to:
IE -> Tools -> Internet Options -> Security Tab -> Click on 'Local Intranet' -> Sites -> Make sure that 'Automatically detect intranet network' is checked.
Now switch to 'Trusted sites' -> Sites -> add your intranet site [if having one web application like me, just add the domain root e.g. http://intranet.company.com].
Staying in 'Trusted sites', click on 'Custom level...', scroll down to the bottom and check 'Automatic logon with current user name and password' as in picture below:
Annoying pop-ups for user credentials should no longer be coming up!