If you don't have a credit card or don't choose to use one, you will be asked for cash or traveler's cheques. They'd prefer that you pay something before you board.
On one cruise, we got a note asking that DD report to Guest Services to make arrangements for her account. DD was 8 years old at the time, and it was their mistake as I had put a card down at boarding...also, she had no charge priv. The note was polite but said something to the effect of since you haven't chosen to give us credit card authorization, we will need to know how you plan to settle your account. Cash, check, trav. check or credit card are acceptable options, etc. I'm sure I don't have all the wording right, but you get the idea. We didn't get the letter till after her excursion charges had posted.