We have gone on over 15 cruises and all have been very safe. The recent problems with cruises are very minor compared to the amount of times they actually go out to see. Major problems like the one that happened in Italy were due to one particular person not taking proper precautions and the rest of the crew not questioning the Captains decision to get closer to land.
I do still get nervous every time we go and worry about everything I hear in the news, but once you're on the ship and go through all the safety measures they present you feel more relaxed.
We also always choose cruise ships with spotless records. NCL is known for various problems so we really never travel with them.
Accidents can happen anyone and at any time. We always have to do our research prior to planning any vacation and make sure we're doing everything possible to stay safe.