You have a few things to think about.
1) Saving money. Student loans are usually at a low interest rate. Thus, if you borrow at a low interest rate and invest into something with a high return, you could save money. However, this contains two big IFs. (A) It only works IF you invest the money and don't blow it. (B) It only works IF you invest the money into something that earns more money than what you pay in interest on the student loan. Few investments are guaranteed, you could easilly put it into stocks and lose money. Just keep that in mind.
2) Being payment free. There is a psychological effect in not owing money. Also not paying a monthly bill saves you time, effort, and costs (stamps, etc). If investing nets you a grand total of $10, was it really worth it for 10 years of paying bills and being in debt? Probably not. Sometimes you have to include the value of having a simple life. Of course, if investing nets you $10,000, then you'd really have to value simplicity to make it worth it to pay off the bill early.
3) Credit. What if you need future loans (car loan, mortgage, etc)? Sometimes it is best not to have too much money borrowed (you could be denied for things later). If you blew your money and still had student loans, you may not be able to borrow enough in the future. Paying off the student loans now would prevent that scenerio.
4) Taxes. You only get a deduction. And you only get a deduction if your income is fairly low. I mistakenly thought I would get tax savings on my student loan. That is, until I realized I was well above the income limit.
It all comes down to your self-control. Yes, with good self-control, and good investing, you are probably better off keeping the student loan. If you don't have self-control or if you won't invest well, or if you value having a debt free life, then pay it off. We probably aren't talking much money anyway you cut it.
Myself, instead of paying off my ~3% loan, I put the money into a house and saved myself from paying 6% on the house mortgage. Student loans are usually good to keep.