With version 10, I get this pop-up window:

Is there a way to let Mathematica use my Windows login credentials, as for instance Firefox does?
With version 10, I get this pop-up window:

Is there a way to let Mathematica use my Windows login credentials, as for instance Firefox does?
Edit -> Preferences -> Internet Connectivity -> Proxy Settings
switch to "Use the following settings" and try
[user]:[pwd]@[Proxyname].[Domain]:[Port]
I had the same in V9 on my work (can't test V10 right now), and it often seemed to be a problem of a proxy using the NTLM protocol for authentication which Mathematica had difficulties with. I found a solution by installing the debugging proxy Fiddler as an intermediate between Mathematica and the company proxy to do the NTLM talking.
However, I just noticed that if you select "Use the following settings:" in the Internet Connectivity>ProxySettings tab and leave all the boxes empty (except the "Port:" boxes which are on 0 by default) everything works without Fiddler. Looks like magic and probably won't work in many cases but might be worth a try.