As of July 15, 2014, you might have problems connecting to Gmail via Outlook and other mail clients such as Thunderbird and Mail apps on (older) smartphones. This is because Google turned off Basic Authentication by default for all new accounts and accounts which haven’t synced within the last 30 days and only lets you authenticate via the OAuth 2.0 standard.
As a result, you’ll get Send/Receive errors (0x800CCC0E) and could get prompted for your Gmail password again in Outlook and the login will fail even when you supply the correct password.
To solve this, you must re-enable Basic Authentication for Outlook in your Google Account Settings. This can be done via the “Allow less secure apps” page where you set it to “Enable”.
Another way to go would be to enable “2-Step Verification”. In that case, you can create a special “App Password” which you’ll then use within Outlook to logon to Gmail rather than with your regular password. This is the more secure approach and highly recommended. For step-by-step instructions to set this up see: Outlook and 2-Step Verification for Gmail accounts.
Native support for OAuth 2.0 in Outlook (2007, 2010 and 2013) is being worked on and hopefully released soon in an upcoming update (I’ll update the this post with the links to the updates once they become available).