Air Pressure sensor
Yes, an air pressure sensor's the way to do it at low cost and with reasonable reliability. You won't be able to guarantee that it turns off as the a/c leaves the tarmac, though (could be some minutes delay) or when it lands (all sorts of reasons why there might not be significant pressure changes at that point). You'll need to detect the descent from cruise and assume that the plane has landed (say) an hour after that.
Obviously, GPS won't work for anything inside the cabin. Accelerometers could be used to assist the pressure sensor to give a better estimate of the current status (air or ground). But it would get reasonably complicated quite quickly if you wanted to be sure of turning your device on/off within seconds of takeoff/landing.
The accelerations during takeoff and landing are extremely variable, and it would be very difficult to design something based only on an accelerometer.
Turning things on (ie after landing?) is usually less of an issue than remembering to turn them off, isn't it? I mean, the user can turn it on, if he's using the device.
Takeoff will generally be easier to detect reliably than landing (always get a gain in altitude of several hundred feet, which the very cheap barometers in e.g. Polar heart rate monitors will detect very repeatably).