Do you have to pay for internet on an iPhone if you have WiFi?

If you have WiFi, which you have logged into (via Settings>WiFi), then you don't have to pay. But if you don't have WiFi/Broadband and are Surfing the internet using a 3G signal then it will charge you. It's often very expensive to simply download a few emails using a 3G signal ... check with your phone company about the prices.

Hope I helped!