Nancy is right - the B.C. must have a raised seal from the issuing state. When my family was preparing for our cruise (Enchantment in August) we discovered that my wife only had a Birth Announcement from the hospital - not an official Birth Certificate. If you go to the states online site, you can probably find directions for getting a certified B.C and it will probably only cost you $10 and takes 3-4 weeks depending on the state. Better to be safe than sorry.
But Nancy's question about when you are traveling is critical. During different stages of 2006, the State Department is phasing in requirements of Passports for areas that use to only require B.C. (i.e Caribbean and Canada).
Enchantment - August 2005