Basically, the money you pay in student loan interest is tax deductible, which means as far as the IRS is concerned, you didn't make that money. However, what that saves you on your taxes is a percentage of a percentage; you save the amount of your current marginal rate on the money you paid as interest.
Simple example with made-up numbers: Let's say you had a student loan outstanding, and you were making payments of $150 monthly on it. Total payments to said loan in one tax year would be $1800. Of that amount, let's for the sake of argument say that half, $900, was interest. You get your 1098-E with that number on it, and reduce your taxable income by that amount. You're currently doing well, not outstanding but OK, so you're in the 25% tax bracket that most single middle-classers are in. So, your reduction in taxable income of $900 saves you the 25% that those 900 simoleons would have been taxed at, which is $225. So, all told, this loan is a net drain on your disposable income of $1,575, of which $675 is pure cost of capital; you never received a dollar in disbursements to match this amount you're paying, so it's money lost now in return for previous gains.
10 years later, you pay off the debt. Now that $1800 is yours to keep, and to pay full taxes on. You pay $225 more in taxes (actually, because of amortization, the amount of additional taxes has been steadily increasing as the interest portion of the loan payments has reduced) but have the remaining $1575 in your pocket to do something else.
While there is good debt and bad debt, debt is debt; whether deductible or not, the IRS will never credit your tax bill in the amount of interest owed (AFAIK; if someone knows of a loan whose interest is a credit instead of a deduction I'm all ears). So, the deduction on this loan reduces your cost of capital to an effective APR of 4.5%, and because it's a student loan and not a mortgage, you don't have to itemize so this is in effect a "free" deduction (even with an FHA mortgage allowing me to deduct interest, property taxes and PMI, and the residual medical costs after insurance of having our new baby, the $11,900 standard deduction for my wife and I was still the better deal this year). But, you're still losing 4.5% per year to interest. That's your break-even; if the money you could use to pay your debt could earn a better return than 4.5%, then invest it, but if not, pay off the loan. Right now, investments that could make you 4.5% are at the bottom edge of a steep increase in risk and variance, so if your expected ROI is close, I'd lean toward paying off the debt.