If you have a loan or credit card balance, and you pay over the minimum due, whatever you pay over goes directly to the principal, right?

The longer you have the debt the more interest you pay as each month more interest is added. If you only pay the minimum you will have the debt for much longer and you will pay more interest. The quicker you pay the debt the cheaper it will be so it is in your best interests to pay as much as you can afford over the minimum each month.

One thing to mention is that with some personal loans with fixed intrest rates, the intrest for the entire term is calculated at the start of the loan and added on to the total. Even I you pay the loan of early you will stay pay the interest for the full loan period.

Should… but check your loan agreement. Some loans have penalties for early payoff.

Not always. As @RealEyesRealizeRealLies says, you need to check the agreement. Sometimes you have to specify on the payment that you want the extra payment to go to principle only.

It depends entirely on the way the contract is written. With our mortgage loan, for instance, we have to state where it goes on the payment receipt.

On our credit card payments, the interest is calculated on the remaining balance, so paying extra would reduce the interest over all.