The Travel Security Administration (TSA) publishes a list of all items that are prohibited in carry-on and/or checked luggage. While various weaponry must be checked, a hair dryer and/or a curling iron are allowed in either case.
It is possible that your airline carrier may have additional items on the list of prohibited items. Southwest and United Airlines both encouraged their customers to double-check the TSA list of prohibited items before packing suitcases. If a bag has not been used recently, it is suggested to go through every compartment to make sure nothing prohibited has been forgotten from a past trip.
If you travel by air frequently, you might want to consider signing up for email notification from the TSA. By supplying your email address on the TSA website, you will be notified by alert when there are any changes to the prohibited items list.