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This is not a Windows 8 Metro app but is worth mentioning. Installing the Chrome browser to the Windows 8 desktop gives full Chrome functionality, including extensions.
Note that if you make Chrome your default browser on Windows 8, you lose the ability to easily access the Metro IE browser. It seems Microsoft has chosen to remove the Metro IE browser from the start screen and even the All Apps screen if you make Chrome your default browser. The desktop IE browser is still accessible but not the nice touch-friendly Metro IE browser.
This app is preinstalled on all Windows 8 tablets and is so good it's worth a mention. The UI is attractive and changes to reflect the local weather.
Choosing a day on the main screen opens up a wealth of detailed informaton about the forecast and current conditions. It makes good use of touch operation.
Weather -- Free (preinstalled)