Arrivals - Customs and Duties for tourist are pretty lenient.  US traveler can bring most anything into the Bahamas for personal use. The exception is fresh fruits and vegetables as well as anything that is illegal in the US. (marijuana, illegal drugs, etc).  Each adult visitor is allowed to bring 50 cigars, 200 cigarettes or one pound of tobacco, one quart of spirits, and a variety of items for personal use such as personal radio,  CD player,  camera etc.  

Customs Departure rules vary by country. US visitors may take home $800 worth of duty-free merchandise. The next $l,000 is taxed at 10%. Gifts valued up to $50 may be mailed home duty-free. One litre of wine, liqueur or liquor and five cartons of cigarettes may be taken duty-free.  No Cuban Cigars, tortoise shell or any item that is illegal in the US.  Customs will usually overlook an extra bottle or two of local rums.  No fruits or vegetables or fresh coconuts.  It's advisable to keep your receipts until you pass through customs.  You'll need to fill out a declaration form with details of your purchases.

For information on other countries, check the Entry Requirements section on the Ministry of Tourism Website (