I have non office application files like images, txt files and if I try to view them in IE11, it redirects me to login screen.
Now there are two interesting things regarding that:
1) There is no problem to view those files in other browsers, like FF or Chrome, so it is not a permission problem in Sharepoint.
2) If I'm running IE as Administrator or with lowered UAC settings, problem disappears (we are using Forms Authentication, so which user is running IE shouldn't impact in any way I guess). I've used Process Monitor to see if I have any access denied issues when I'm running IE as regular domain user, it could not access some registry keys, I've added access to them just to make sure that it is not root of the problem, so those events with access denied disappeared, but that didn't fixed the problem.
3) I can open any office files, like docx without a problem using IE.