What's the best way to remove stick-on frame protectors I need to move a couple of frame protectors from the head tube of my bike but don't want to damage the paint in removing them. What's the best way of getting these off?
It depends on the type of adhesive. Sometimes it can be just pulled off. Sometimes the gentle heat of a hairdryer (not a heat gun) can weaken an adhesive and make it easier to remove. 

Or you can try the use of GooGone or similar adhesive thinner/solvent (try on an inconspicuous place first to make sure it won't damage the finish).

Heat and solvent cover 90% of cases. 

If the protector was epoxied on, then it is very hard to take off without damaging the finish.