I am a travel agent and cruise specialist - you will need a certified copy of your birth certificate, issued directly by a government agency. A copy is not acceptable. You will also need a government-issued picture identification, such as a driver's license, and official, certified government documentation of any name changes from the name listed on your birth certificate, especially for women who use their married name and who could use their official certified marriage license.
The others are right...a passport is the BEST way to go. It is a lot less to carry with you when you travel and it is a quick and easy during the check-in process.
Have a great day!