I have IPv6. Why does my connection to the Windows Store fail?

Try if your store is working after EACH of the fixes below, until it's working

Make sure internet is working (duh)

Check if you can connect to websites. If you can't, try the following:

Press win + R and type inetcpl.cpl.
In the window that appears, click on LAN settings.
Check "Use Proxy Server for your LAN" is unchecked like this:

Check your date and time

Again, win + R and then type RunDll32.exe shell32.dll,Control_RunDLL timedate.cpl

Internet time -> Change settings -> Update now

Windows Services

win + R -> msconfig

Click on Diagnostic Start Up then reboot.

Use your Local Account or another Account

Try registering for a new one if you have just one.

Last resort: refresh

win + C -> Change PC settings -> General -> Refresh your PC

Source

This was eventually traced to an IPv6 routing issue with CloudFlare's network, and was affecting many other CloudFlare IPv6-enabled services as well. CloudFlare or its upstream providers have since resolved the issue.

(Though as of now they've screwed it up again...)

I have AVG and did the upgrade at work and at home to Windows 8 pro and on both machines I was unable to access the app store. After reading about the IP addresses and ports above I immediately thought "maybe my firewall is blocking these connections". So, I opened up AVG and turned off the firewall and BOOM I was able to connect to the app store. I then clicked on the "Regenerate Firewall Settings" within AVG and tried to connect to the app store and no dice. So, I disabled the AVG firewall for now and activated the windows firewall until I find a fix for AVG.