If you are only interested in arriving at your resort destination and staying put, by and large you will find Jamaica perfectly safe, although aggressive beach vendors can sometimes intimidate. Guided tours arranged by resort staff are the safest way to get out and see the country a bit without too many security concerns. And many visitors to Jamaica find that the backcountry areas of the island are friendly and welcoming.
On the other hand, as the latest U.S. State Department missive on Jamaica notes, parts of Kingston (Mountain View, Trench Town, Tivoli Gardens, and Arnett Gardens) and Montego Bay (Flankers) are some of the most dangerous places in the Caribbean outside of Haiti. Even well-traveled U.S. Embassy staff are advised to stay out of certain neighborhoods in Kingston, especially after dark, and to avoid using public buses that can be overcrowded and targets for criminals.
The Consular Information Sheet from the State Department contains important information to ensure that your next trip to Jamaica is a safe and happy one.