One security precaution is to strictly enforce ID requirements. In order to be allowed onboard you must produce a valid government-issued photo ID (such as driver's license) and an original or certified (not photocopied) birth certificate. If your name has changed you must also provide an original or certified document of that change (true for married women, for example). A valid passport can replace these items.
Another is that if you are stopping at a U.S.(or U.S. territory) port after being in a foreign port, all passengers are required to meet onboard with immigration officials before being allowed onshore.
As far as luggage is concerned, precautions are similar to the airlines' - as most cruisers fly to the port of embarkation anyway, this is not a big deal for nearly everyone.
Basically, make sure you have proper ID, and otherwise just relax and enjoy yourself!