It gets even worse as Gogo designed its network specifically with law enforcement requirements in mind, which further limits your privacy options. Gogo blocks secure HTTP connections and together with Global Eagle it also appears to block VPN traffic. ARS Technica offers some advice on how you can safely use in-flight WiFi:
So how do you protect your privacy and still stay connected?
If you can get a VPN connection to work, use it. Make sure you've enabled the firewall software for your computer and that you've turned off any sharing services. Check the certificate of secure websites. Chrome and Firefox will usually catch forged or proxy certificates. If you get a certificate warning, don't click through to continue—wait until you've landed and have a safer network to work from.
And if all else fails, just turn off Wi-Fi and work offline or enjoy the flight the way millions before you have—by staring into space or thumbing through that in-flight magazine.