I started my Mail App and found it stop working, an error log was found in Event Viewers, which stated:
"Activation of app microsoft.windowscommunicationsapps_8wekyb3d8bbwe!Microsoft.WindowsLive.Mail failed with error: This app does not support the contract specified or is not installed. See the Microsoft-Windows-TWinUI/Operational log for additional information."
It seems this error is common for a lot of Windows 8 users, but there's no fixed solution for this probem. In my case, I have a solution that finally fixed it