After some searching on Google, I ask myself:
Is it possible to build a compass (simple showing the heading/direction) with
the iPhone 3G’s GPS sensor?
I have the suspicion, that this is only possible, if the device is moving.
Any ideas are appreciated.
Yes, you are right, that’s the only way. Although I think once you know the direction, you could track small movements of the phone from acceleration sensors and draw the direction accurately even if the original movement stops.
Note: This is outdated info, it was correct up until 3Gs came out. Unfortunately I can’t delete accepted answer so just look below.