We've been to Jamaica many many times and have never had any problems. However, that does not mean you won't encounter some.
It's like anywhere else - if you go looking for problems, you'll find them. So just be smart. This applies to everywhere in the world that you may go.
For the most part, as long as you stay within the 'tourist' areas or take an organized tour, you'll be fine. This does not guarantee you'll have a totally safe experience, as we do hear and read stories about bus loads of tourists being robbed - even those excursions offered directly by the cruise lines. While this is relatively rare, it's also not just limited to Jamaica.
There are some wonderful independent tour companies, such as Shore Trips, that offer very good excursions. Personally, we much prefer them over the cruise lines anytime.
We once hired a taxi for the whole day and had him drive us around to places most tourists don't get to see. We had an incredible day and got to meet some wonderful people and ate some great food.
But having been there many times and seen it all, we now just like to purchase a one-day pass at an all-inclusive resort where we can enjoy the wonderful facilities, the beautiful beaches, the awesome Jamaican food, and the service while relaxing in a very safe environment.
But deciding not to go on a cruise because it's going to Jamaica or deciding to stay on the ship for fear of not being safe does an injustice to the wonderful people of this beautiful island.
It's like I always say, don't listen to what others say because otherwise you'll miss out on alot.
If people listen to the news about all the murders in Washington, DC, you'd never want to come here. And yet I've lived here 54 of my 62 years and never had any problems whatsoever. But if you park a new car with a brand new camera on the seat and the doors are unlocked with the windows down in certain parts of the city at 3:00am, I guarantee you the camera will be gone in 10 minutes and more than likely so will the car. But if you stay in the tourist areas, this is a remarkably wonderful city to visit. The same can be said with hundreds of places all over the world, including Jamaica.