Bottom Line: Payback
A number of factors go into deciding whether to refinance an existing mortgage, but one of the main considerations is the payback period on the refinance. (Assuming you don't decide to refinance for other reasons, like to convert an adjustable rate mortgage into a fixed-term mortgage, or to get a loan with a significantly shorter term, or because you wish to take cash out of the equity in your home to use for other purposes.)
To calculate the payback on refinancing to get a lower interest rate, simply divide your total costs to refinance the mortgage (fees, points, closing costs, etc.) by the amount your monthly payment will be reduced each month. For example, say your total costs to refinance are $4,000 and you will save $90 per month; it will take 44 months, or nearly 4 years, for you to break even on the refinance. Stay in the home for more than 44 months and the refinance makes good financial sense; sell the home in, say, 2 years and you will have lost money on the transaction. All other considerations being equal, focus on the payback period to help you decide if refinancing into a lower interest rate makes sense.