Although Negril is one of the safest destinations in Jamaica, thefts are not uncommon. You should take care on the beach, especially in public areas. Some of the more upscale hotels have security guards who will take care of your belongings. If you are staying in a cheap property, leave your money and documents in a safe box and never open the door to strangers. At night take a private taxi, and avoid walking on the road.
The main problem in Negril is the drug traffic. If you are not interested in drugs, just say "no, thanks". Ganja (marihuana) and cocaine are offered on the beach. But these are illegal drugs in Jamaica, and penalties are severe. Refrain from smoking ganja on the beach, because undercover narcotic police patrol the beach.