US Dollars are widely accepted in Jamaica, and seem to be preferred.  Just don't expect any small change back.

I've never had any problems paying for anything in US dollars, and any business has a calculator handy to do the conversion.  Any change due back to you must legally be given in Jamaican currency.  Sometimes, you can press that your change be given back to you in US currency.

The official exchange rate in December, 2005 was about J65 = US$1.  At the gas station at the Montego Bay airport, we filled up our rental car (it was given to us empty), and were given a rate of 50 to 1.  60 to 1 seemed to be the official "unofficial" exchange rate most everywhere else at the time, used everywhere from grocery stores to jerk stands.  You can change money at any "cambio", look for the signs or ask someone.  We changed money at the grocery store regularly.  The rate can be slightly different - a hardware store gave us 62 to 1; that old Jamaican favorite, KFC, offered 59.  (Me eating KFC in Jamaica? Are you kidding - I just needed a cool drink.) It wasn't a coincidence that the drink was J$60, and the manager offered to exchange a dollar for J$59.  Another patron exchanged my USD for J$60.  On a prior trip, our driver took us to the Montego Bay craft market to exchange money at a very favorale rate.  

Several times a vendor made a  "mistake" doing the mental conversion calculation whether by accident or intentional.  If it's important to you, as it is to me, to not feel taken advantage of, always do the math yourself, state the US price, and gently insist when you are correct.  Tipping should be optional and at the purchasers discretion.

Cash and other negotiable instruments in amounts greater than US$10,000 brought into or out of the country must be declared at Customs.

There are ATM's at banks and many gas stations.  Be aware of your surroundings and try to avoid out of the way ATM's at night - just as in the US.  Many ATM's require you to insert your card to open the door to the ATM room - assuring your privacy and security during your transaction.  I have had trouble opening the door with my US ATM card; once I had to have a Jamaican swipe their card to open the door, but my card worked fine in the machine.

There is a USD ATM machine in the departure terminal at the Montego Bay airport.

Be aware of your financial institutions fee structure for foreign and foreign denominated withdrawals.