Changing the term of your mortgage can help in several ways. First, if you were to refinance your current mortgage from 30 years to 15 years, you will accelerate the rate at which you pay towards principle each month meaning your house will be paid off quicker. Also, you will save an unbelievable amount of money in terms of interest because you would likely be taking 10 to 15 years off the life of your loan. Second, you can also refinance a 15 year mortgage to a 30 year mortgage. It seems like it might not make sense to do this, but if you have an immediate need to free up monthly cash-flow and you don't want to take out a home equity loan, this can work out to your benefit. When you take a 15 year loan and refinance it to 30 years you will have the same balance only the payments can be hundreds of dollars less than the 15 year loan. The only draw back to this is you will pay more in interest over the live of the loan.
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.
Make sure that your original mortgage does not have a pre-payment penalty or early payoff penalty of any kind. Sometimes people will get into their mortgage with the mortgage having a pre-payment penalty and they will not even know about it. Pre-payment penalties usually range from 6 months to 3 years with a penalty for an early payoff. The penalty is usually about the amount of 6 months worth of your mortgage loan interest, but this varies. You would have to be able to have some significant payment and interest savings on your refinance loan to justify refinancing a mortgage loan with a pre-payment penalty.
It is feasible to go for a refinance when you have built up at least 10% equity in your home (For Fannie Mae owned mortgages, the value is 5%). It is also possible for you to choose the option if your equity is less than 5%, but you may have to pay a certain amount of cash in order to make up for the difference in equity.