How deep must holes be dug for footings on a deck?

It depends on what zone you are in. Ask your local building inspector, or google your state building code, which hopefully will be the same as your local code.
Lumber yard staff will probably know too, or any contractor.

And beware - most localities will require a permit, and if you don't get one, they might make you dig up the piers down to the footings.
Also a deck will increase your property tax valuation.

I agree with Joypulv, they will vary significantly if you are in Texas as opposed to North Dakota. There is a very good reason for the depths they are established at for your area. The places previously mentioned will have the local code for you.

North Pole or Equator? Below frost line for sure. You may or make not need a permit. Where I live, 200 sq. ft or less and 30" or less from the ground does not need a permit.