Originally Posted by FBinNY

If you have a typical welded frame with a thin-walled headtube and pressed-in headset I suspect that you might have some bellmouth in the lower headtube.

This isn't rare in well used mountain bikes, as the continual pounding stretches out the tubing allowing some movement of the headset cup in the frame. It's this very problem that was a major factor in the movement to integrated headsets.

If your tube is bellmouth you'll notice that the force to press in a headset is reduced, and there is no real cure since you can't shrink the tube back to size. You can get rid of the creaking by using some bearing retainer when mounting the cups (this will make removal more difficult). I've also had success painting the pressed-in section of the cup to build up the diameter a bit. If you try this, use a piece of paperboard with a hole in it as a mask to prevent overspray and be sure to allow the paint to cure until fully hard before pressing in.