Rules regarding packing razors in airplane luggage depend on the type of razor in question. Disposable razors and cartridges are allowed in carry-on bags, while most other types of razor must be secured in a checked bag.
As of May 2014, the Transportation Safety Administration (TSA) allows passengers traveling within or from the United States of America to pack certain kinds of razors in luggage that is brought on board commercial airliners either as checked luggage or a carry on. A good general guideline is to consider whether an item can be used as a weapon. If the answer to this question is "yes," these razors, including box-cutter blades and safety razor blades, cannot be brought on board in a carry-on bag. Those who must bring these items with on their trip may check razors in luggage if they are wrapped to protect baggage handlers. Those who don't want to check a bag should stick with disposable razors, which are allowed in the main cabin.