[Manichean]

Okay, because we're seeing many help requests concerning this, I just went ahead and tested it using the configuration Calibre generated by pressing the big, helpful GMail button from a machine I know can send GMail via SMTP (I use it in Thunderbird). No problems.
If your configuration is correct otherwise, which is likely if you used said GMail button on the configuration page, there's something preventing Calibre from reaching the GMail server. Most probably it's a firewall of some sort. If you have configured your PC's firewall to allow Calibre access, there's still the possibility that your router, for whatever reasons, block SMTP to GMail servers (can you send mail via GMail from, say, Thunderbird or Outlook?). The last possibility is that your ISP prevents SMTP servers other than its own from being reached, which is not totally unheard of, though still incredibly rude, if you ask me.
It would help, for further troubleshooting, if you'd confirm that your settings are correct. (The working settings for me are smtp.gmail.com on port 587, TLS enabled. Your username should include the @gmail.com or @googlemail.com, though you'd get a different error if that was the problem.)