Should I keep a balance on my credit cards to improve my credit score?

From FinancialPlanning

No. The total amount that you currently owe, relative to your total credit available, is one of the factors that affects your credit score. So keeping a balance on a credit card should hurt, rather than help, your credit score.

Another point sometimes mentioned on MIFP when this topic comes up is that keeping a balance on a credit card is itself a questionable practice, because you'll pay interest on your balance each month -- typically at very high annual rates (12% to over 20%). Avoiding credit card interest is a more important financial goal than improving a credit score.