How can I remove the moulding from my wall without damaging either the drywall or the moulding?

A pry bar is more efficient than a claw hammer, and its smooth base keeps it from damaging the wall.

Check your state and local codes before starting any project. Follow all safety precautions. Information in this document has been furnished by the North American Retail Hardware Association (NRHA) and associated contributors. Every effort has been made to ensure accuracy and safety. Neither NRHA, any contributor nor the retailer can be held responsible for damages or injuries resulting from the use of the information in this document.