Travellers are not under any obligation to use a padlock when they fly but many people choose to use a travel padlock for peace of mind.
If you do decide to use a padlock with your luggage it is not necessary to use a TSA Approved padlock but bare in mind that if you don't use one and security officials decide that they wish to inspect your baggage there is the very real possibility that the luggage could be damaged which might be very costly. For this reason it is a good idea to use TSA Approved padlocks.