Do: Refinance for the same term as your outstanding loan
Think of your mortgage as a building that's 30 stories high (or, if you have a 15-year mortgage, the building is 15 stories high). Your goal is to pay off your house by getting to the top of the building, one floor at a time.
With a refinance, don't start again at the bottom floor. Stay on the same floor. Keep climbing from there.
Let's say you are five years into a 30-year mortgage, and you're refinancing into another 30-year mortgage. You planned to pay off the old mortgage in 25 years, so you should plan to pay off the new mortgage in 25 years, too. It's easy to do. Just ask the lender to amortize your payments over the shorter term.
Or, if you can afford it, refinance into a 15-year mortgage.