The only reason to pay them off is to have the peace of mind that you're debt free. It may not be the most financially advantageous thing to do, but it may be worth it if she won't stop hounding you.
She's a GF not a wife. If she's hounding you that much now, how much will she hound you when you marry her.. I'd show her interest paid, versus interest earned..
Your interest rate on the loan is less than that of inflation, so you are basically getting free money as it is. I also try to stay debt free, so if you can pay it off it might make sense from a debt perspective not to have that debt, but as others have said. Student loans are the most forgiving loans. You'll never get another one like it, especially at that interest rate.