It depends. You need to consider several factors, such as how long you will stay in your home after you would refinance. If you can save money on interest rates that were considerably higher than they are now, then do the refinance to lower your monthly payments as long as you can stay in your home for a reasonably long time. If you will be moving in a few years, the month-to-month savings from refinancing may never add up to the costs that are involved within that short timeframe.
Refinancing also depends on how much the refinancing will cost you. With new, low-cost refinancing packages, it might make financial sense to refinance at even a half percent difference. Have your lender “run the numbers” given your particular situation and payment, and include the closing costs of refinancing to see whether you will come out ahead.
Another reason to refinance is to convert an adjustable-rate mortgage (ARM) to a fixed-rate mortgage. The ARM might have been a good rate when you first got the loan, but if current rates are around the same as they were back then, you might want a predictable monthly payment on a fixed-rate mortgage.
Also, some people are refinancing to a shorter term, say from a 30-year mortgage to a 15-year mortgage. Your monthly payments will be a little higher, but your overall interest costs will be substantially lower. If current interest rates are lower than what you are paying on your existing mortgage, your new monthly payments might not go up much at all. Refinancing to a shorter term is a good idea if you are close to retirement because a shorter term loan means you will probably own your home before you retire.