It really probably depends on the type of debt that you already have and what the interest rates are. If you have a car financed at 0 or 1.9 percent, for example, why pay that off? On the other hand, if you are paying 10% or more on that loan, get rid of it. If your car payment is extremely large, you might want to pay it off no matter what the interest rate is. Credit card debt tends to be high interest, so get rid of it because it is costing you too much money every single day. Student loan debt at the federal interest rate you can probably not pay off because the interest is low and if you became unemployed, you could defer your payments or lower them if you had to. Private student loan debt, however, could have a much higher interest rate and you will benefit from paying it off. Start reading about debt to income ratios so you can understand how you will qualify for the best interest rates.
I have a fairly straight forward aversion to debt; however, to me it doesn't make any sense to pay off debts with interest rates below 5% when you can be maxing out an IRA and earning 10% or more. And with a Roth IRA, you can withdraw the money you put in without penalty.
However, the higher your credit score is, the better your interest rate will be and that could save you tons of money over the next 30 years. Without more information on your actual situation, hard to know what to recommend. What is your credit score now? How much debt, what kinds of debt, and what are you paying in interest? What is your debt to income ratio? Don't just go into the decision to pay debt or save based on a guess. Study, learn, and then react.