I know a refi allows you to take advantage of a lower interest rate, which means a smaller monthly payment even after you factor in the fees and closing costs. But does it also mean you will have to extend the amount of time you are paying the loan? Or is there a way you can also reduce the term of the loan.

IOTW, are you paying the price of being in a mortgage essentially forever, and the only benefit is a smaller monthly mortgage payment?
All else being equal, I would prefer to pay as much as possible but to get out from under the obligation as soon as possible.

I realize everyone's situation is unique, but when I bought my house, I calculated the total cost (principal plus interest) and got as short a mortgage as I could afford monthly payments for that would minimize that sum. No one can afford to pay cash for a house, you have to borrow, but I felt minimizing interest was my top priority, not minimizing the payment.