Most cruise lines and other government officials make sure that the passengers' safety / security is the main priority. At the terminals, you must show ID and proof of citizenship to board, similar to at the airport.
I've only been on 3 cruises, but on all of those, I have never felt unsafe. If bad weather interferes with a cruise, cruise lines will either revise the ports of call to sail around the bad weather, or cancel a port altogether.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)