If you are refinancing from one ARM to another, check the initial rate and the fully-indexed rate. Also ask about the rate adjustments you might face over the term of the loan.
Refinancing is not the only way to decrease the term of your mortgage. By paying a little extra on principal each month, you will pay off the loan sooner and reduce the term of your loan. For example, adding $50 each month to your principal payment on the 30-year loan above reduces the term by 3 years and saves you more than $27,000 in interest costs.
If there are only a few years left on your current loan, it's no use refinancing with a long term loan. You may need extra cash but with a long term loan, you'll end up paying more for the entire loan term.
Resist "no cost" refinancing. No cost doesn't mean free. On the contrary: The closing costs are usually bundled into the new mortgage, which means you pay interest on them. The fees associated with a 30-year mortgage could cost you more than double what they would have had you simply written a check for them at closing. Or, if the costs aren't bundled in, you'll be charged a slightly higher interest rate. Either way, the lender wins.