Mail app for Windows 8.1 - Enable/disable email notifications
Learn how enable or disable email notifications in the Mail app of Windows 8.1
Note that: If you are using multiple email accounts with the Mail app, then you will need to edit this option for each of your accounts:
Open the Mail app.
Press the Windows key + C to bring up the Charms Bar.
Click on Settings > Accounts.
Select the account of your choice (if multiple).
Click on the "Show email notifications" menu and make your selection: