Okay, I have to chime in on this one as well, having been to Jamaica twice, the most recent trip just completed in July 2002.
1. Expect to be offered drugs (usually pot or cocaine, but nothing is out of the question). Politely decline and keep moving -- you are not obligated to have a conversation with this person. Unless, of course, it is a uniformed, armed, airport security guard offering you the "smoke, mon" (happened on our first trip there!)
2. Stay in a nice resort. Stay AT the nice resort. Security is good, and the people who get robbed typically are being too "adventurous" (meaning by themselves without a guide, usually in the mountains or less populated parts of towns). By the way, one of my co-workers was jumped last night by 4 guys, in Scottsdale, AZ (supposed to be a nice city with low unemployment, no apartied, etc) and is recovering in the hospital. No country has a monopoly on crime or bad people!
3. Bring your own gear. Even the nicer resorts don't tend to maintain the gear very well. Remember that, because they are typically all-inclusive, including the diving, they cater more to first-timers than to certified divers.
4. There is some nice diving, BUT...
The waters there are severely overfished, and the coral continues to suffer lots of damage. The first is a result of the current economic conditions there, the latter seems to be a combination of some disregard by the local lobsterers and too many "resort divers" running into them.
In summary, I would go back to Jamaica -- as a family vacation destination with lots to do for a very reasonable price. I have met far more good, decent people there than bad people, and have always received good service. The diving is not the best in the world, but the water is warm, viz is usually excellent, and you will see rays, turtles, eels, dolphins, etc. Just like anywhere (including the good ole US of A), there IS crime. Be smart, use common sense, and you will significantly lower your risk of becoming a victim.
Thanks for letting me ramble on...
Scuba Legs