The Geneva Airport has free WiFi. The one catch is you need to have a mobile phone to get it. When you open your computer or mobile device's browser you will directed to where you can input your mobile number.
This doesn't have to be a Swiss mobile, an international one will work. You just have to be able to receive an SMS. You will then receive a code by SMS to let you log on. Once logged on you will have access for one hour. Once your hour is up you can request another hour, again free of charge.
The network is identified as 'Free_WiFi_GVA' and should be accessible from most public areas of the airport.
Here are some screenshots that demonstrate how to get WiFi at the airport up and running.
Swisscom also offers a paid WiFi service at the airport.