I originally tried to update the issue that is described here, which I'm also having. Unfortunately that edit got rejected, so I guess I have to write my own question.
When I try to log in to Stack Overflow on my newly installed Windows 8 machine, nothing happens. I can click on the OpenID provider buttons, but the page is not redirected. In the background, a JavaScript exception occurs.
The issue is being caused because a JavaScript tries to access window.localStorage, but this raises an exception:
openid-jquery.js, line 9 character 73
SCRIPT5: Access is denied.
Most likely, an exception when trying to access this property should be treated as if local storage is not supported by the browser at all.
What is causing the access to be denied, seems to be the Protected Mode option in the browser options. This is enabled by default on my system:

If this doesn't give a sufficient repro case, the problem might be reproduced like this, however this is not what is happening on my system. Process Monitor does not show any failing file access, and Enhanced Protected Mode is not enabled.
Obviously, I do not run my browser as Administrator by default (nor do I want to), but doing so would allow the login, regardless of this checkbox.
I also have another Windows 8 machine at home, for which it works out of the box. On my work Win8 Enterprise machine (on which I did not enable compatibility view), it does not.
<meta>tag can be added to the HTML to disable compatibility mode.<meta>tag won't have side effects with other, well-supported browsers?