If you are able to get a lower rate that what you currently have, you can save tens of thousands of dollars over the life of your loan. Also, most lenders don't charge as many fees to refinance a mortgage and depending on how much equity you have in your home you may be able to roll the closing costs into your new loan, still have a lower balance than your original loan, a lower rate, and a lower payment.
Know your credit score before you begin looking for a loan. If you can, try to remove any blemishes from your credit report before applying for a refinance.
Carefully review the estimated closing costs. If you decide to lock in the rate, the lender will send you a "good faith estimate" of your closing costs within three days. Go over the numbers carefully, and compare them to the ones that appear on the final settlement statement (the HUD-1) from your previous mortgage.
If there is a big difference between the initial interest rate and the APR listed in the ad, it may mean that there are high fees associated with the loan.
It's better to follow the 2% Rule which suggests that you can enjoy the benefits of a home refinance if your mortgage refinance rate is 2% lower than that on your current loan. The interest savings will help you recoup the costs you've paid for the new loan provided you stay in the property for a certain period of time (break-even period). However, there are no-cost as well as low-cost refinance loans wherein the costs are included into the loan. But you can expect comparatively higher rates on such loans. Moreover, these loans are limited when the market is in a credit crunch.