It depends. There are lots of things you can spend extra on, or you can avoid the extra stuff. What I can think of that's above the cruise fare is:
Gratuities: recommended is $12 per person per night.
Room service tips: Most items from room service are free but I always tip a few dollars to the CM who delivers the food.
Alcohol: This depends on how much you drink. It can add up. There are drink of the day specials that run about $5/drink. You can bring onboard up to 2 bottles of wine or 6 beers per adult (21 or over) at embarkation and at each port.
Pictures: The photos aren't cheap. You can pre-purchase a package of all digital photos for a discount or purchase smaller packages onboard.
Port Adventures: Varies in cost. With the exception of
Castaway Cay, you can choose to book with outside vendors and pay less than what
DCL charges.
Specialty coffees from Cove Cafe.
Adult dining.
There's no set amount of money that DCL requires to be available. If you don't want to tie your credit card to your onboard account, you can fund it with cash or gift cards.