Does closing accounts lower or increase one's credit score, or does it depend?
If you mean closing credit card accounts it will hurt your credit score in two ways:
1) It will reduce your available credit, which in turn will increase the utilization percentage of your credit if you owe a balance on any other card.
2) It will reduce the average age of your open accounts unless it was the last card you obtained.
I do believe that closing your accounts could affect a negative credit score. If one does not have some credit card history, they assign a lower score to your ratings. I have problems because I don't have any large purchases that I am paying down.
It is okay to just keep your accounts at a zero balance.