Cigarettes - you are allowed to bring these onboard any ship but the Carnival Paradise (a completely nonsmoking ship), and there is no limit to the amount you can bring onboard.
The alcohol policy depends on the cruiseline. Most cruiselines allow you to bring wine onboard, but charge a corkage fee if you want to drink it in the dining room. Most cruiselines also prohibit or "reserve the right to limit" alcohol brought onboard. This means if you try to bring alcohol onboard, it may be confiscated. Many people do bring it onboard with no problem, but it's at your own risk. Please check the Frequently Asked Questions page of your cruiseline to find out their individual policy.
If you choose to buy duty-free cigarettes or alcohol on the ship or in the ports, though, there is a limit to how much you can bring back. This brochure from the U.S. Customs Department will help you know how much you can bring back with you. The cruise director will also tell you during the debarkation talk.
I recommend you get a booklet from the U.S. Custom Service "Know Before You Go:". Write for copy to Department of Treasurty, U.S. Custom Service, Washington, D.C.
If you are on the Internet you can download and copy the information via http://www.customs.ustreas.gov/travel/know.htm