Windows 8 Mail app doesn't work with Gmail when 2-step verification is enabled

There is actually a simple way to get your GMail acount to work with Windows 8 Mail App even with 2-step verification enabled. You'll just have to use Application Specific password.

1. Go to your Google Account settings. You must be logged in: https://www.google.com/settings/account
2. Click on Security from the Accounts tab.
3. In the Authorizing applications and site section click on Edit button
4. Scroll down. At the bottom you'll see the section Application-specific passwords. Type a Name click on Generate Passwords.
5. You'll be given a password. Use that password with Windows 8 Mail App.

Another possibility is that it's failing because Google recently deactivated Exchange ActiveSync for free Gmail accounts. Try un-checking the option to include contact and calendar data, which makes the Mail app use IMAP instead of EAS.