When arriving in the Bahamas visitors need to go through customs.
People traveling by air:
Your luggages may be inspected by officers. As long as you bring anything for your personal use you should not have any problems unless you bring vegetables or fruits. Items that are also illegal in the US such as illegal drugs cannot be taken with you as well. Customs agents are usually pretty lenient but you still can be checked. As long as you are pretty reasonable they will not bother you. It is not uncommon to see people traveling with meat, fish, cheese and it is perfectly fine. People can legally travel with a bottle of wine or liquor, custom officers can overlook if you have an extra bottle but they may also ask you to pay duty on the extra bottle.
People traveling by boat:
When clearing customs at the first port of entry an inspector may visit your boat. As long as you go cruising you can bring whatever drink or food including vegetables that you will consume during your escapade.
If you arrive by boat customs agents may jump on the boat to proceed to an inspection. A smoker can bring up to 50 cigars and 200 cigarettes. It is suggested that you keep receipts with you just in case you are being checked. There is a $ 100 duty free exemption per person.