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To remove the tape from your glossy painted doors, sponge the tape with vegetable oil to loosen the adhesive. Let it stand for several minutes. Using a dull knife, work cautiously and slowly to remove the tape. Continue to apply vegetable oil to any adhesive that remains as you are removing the tape.
this works well on labels on glass doors
Avon "skin-so-soft" will also work for all things gummy and sticky including gum in hair.
A blowtorch can also be effective
If you are able to use Peanut Oil it is far more effective at breaking down adhesives and especially gum in hair. It is easily washed away after with a little Ajax dish detergent and it's wonderful super degreasing formula.