As a student, I'm curious to see if I can put my tuition on a card... That would be useful. :-)
I think most schools are charging fees now, though. There used to be a scam where you could massively overpay you tuition bill on a credit card and then the school would cut you a check for the difference. (Lots of people legitimately end up overpaying because grants or loan dispersements can hit your account at weird times)
You can however charge your federal income tax (and some state income tax) payments against your card for a fee.
American Express even lets you use rewards points to offset this fee.