To make a call from an airplane, your only real option is those phones on the seats you have to pay for (and even those are rare now). Using your cell doesn't work, and neither does VoIP as it's often blocked by Wi-Fi providers. You know what does work? The iPhone 4's video chat component, FaceTime.
At least, it works for now. The Unofficial Apple Weblog managed to put through a call to someone on an airplane and the connection is pretty solid, all things considered. Personally, I bet the days of this working are severely numbered, as the ban on cells and VoIP in America isn't a technological consideration. It's just policy.
Check it out in the video below.