Don't refinance unless you plan on staying in the home for another 3-5 years or it will save you so much in interest during the next 2 years that it will cover the cost of the refinance. These are great times for mortgage rates and everyone should be looking to refinance if they have not done it in the last 3 years or so. I like the option of the 15 year mortgage because again you get a better interest rate than the 30 year on top of the fact that you would pay much less interest even if you had the same rate in either amortization schedule. You can still choose to do the 30 and just add the additional payment each month to make it like a 15 year loan. The only problem with this is that most people do not have the discipline to do this, there is always going to be something that tells you to stop making those extra payments, like a vacation, a car, big Christmases, birthdays, home remodel, etc. If you decide to it this way you should always have a back plan. (you should be doing this anyways)
After you have rid yourself of all consumer debt you should always have 3 different types of savings and do them in this order. 1. 3-6 months emergency savings in the case of hardship, job loss, leaky roof, etc. These funds should be fairly liquid. 2. Retirement should be 15% of your gross income. There are lots of ways and theories to do this but that is for another discussion. 3. Big purchase savings. Things like the car, vacation, remodel. you get the idea.
The important thing is to remember that these funds are not to be confused. Your emergency money does not turn into your big purchase money. Once savings 1 and 2 are in place and being built any extra cash flow can be used for savings number 3 or paying off the mortgage early or saving for kids college or a mixture of savings number 3, house and college.
That is my opinion and it has helped a ton. You can change your family tree with this personal finance plan. If you have additional questions let me know.