I like to keep a zero balance on my credit cards thus pay off the amount in full. I recently had some refunds on items purchased so my credit balance is negative. If I take a cash withdrawal on the credit card -- will they still charge a fee? I want to cash out the money since I want to close the card.

Yes they will do Not take the money out of a machine on it, ring them and tell them you wish to receive your balance and they will do what's needed.
Cash withdrawl on a credit cards are normally charged at a much higher rate than purchases so go careful.

Why not just go out and use the credit card to buy other things you need? That will get rid of the credit balance.

And why are you going to close it? It seems silly to close a card that you have a credit history with.