You don't need anything other than your passport and a separate photo id, like a state issued driver's license or id card. Although as I type this, I recall that a few states do no have photos on their Dls.
Assuming you are a US Citizen:
Having the passport issued means that the Department of State is convinced that you are a US Citizen and have the birth date that is listed. It means that the burden of proving your citizenship has been assumed by them and that the person at the checkin counter doesn't have to worry if the raised seal on your birth certificate is authentic or not. They don't have to try to read something that is blurred because it was in a fold of the paper or whatever.
I applied for Passports for my DW and myself in February so that we could carry just the passports and a separate photo id. I believe that it gives more security for ourselves and also for the person that is reading it, such as the customs personnel or even the
DCL checkin agents. The person reading it can presume that it's valid if it looks unaltered. I though that I read somewhere of a database that has info about where a person has been by having their passport stamped and the barcode scanned, but it must just be for countries that require a visa or something like that.
Anyway, that's why I paid the fee to get them, so that I could prove citizenship and identification more easily and to remove the guesswork from reading my birth certificate.
To play it safe with our passports, I'm going to make two copies of the first pages and put them in different suitcases. I also read an excellent idea from another poster that said she scanned the first pages of her family's passports into her pc. Then she sent an email to herself with an attachment of the scanned image so that she could retrieve the info by printing it out, from anywhere in the world. You just need to make sure it is an email address that can be accessed using the Web and not application software. Hotmail and Yahoo mail are examples of web based email systems, and there are many others.
If you aren't a US Citizen, then a corresponding department in your country would have the same responsibilities as the Department of State does here.
hope that helps