The first option is to pay it off as soon as possible. If you have a lump sum of money, you can apply it to your mortgage. Or sometimes people will send an extra amount with their monthly payment. This feels good emotionally because you don't have that monthly bill coming in. There is something nice about not paying somebody interest. Some people chose this option because they hate the idea of debt.
The second option is to get a 15 or 30 year fixed mortgage and pay the house off over time. You can leverage your money and, by paying less per month, you have money to invest for your retirement. This appeals to those who think logically.
So which is best? The answer is: It depends. If you have plenty of money saved for retirement, go ahead and pay that house off. If your goal is to increase your net worth, paying the house off over time makes more sense.
When you are paying the house off over time, you are freeing up money to save for retirement, college, or other planned expenses. By putting money into your retirement account rather than giving it back to the mortgage company, it can grow for you. See my article on Time is Money. Money in your retirement accounts can help feed you in retirement, while money in your house can not.
Many seniors are house rich, but cash poor. How can this be? They don't have a mortgage, but unfortunately they have not saved enough in retirement accounts to generate extra income for living expenses. These days, people in this situation are having to resort to reverse mortgages. A reverse mortgage can be an expensive way to take money out of your home. It can also deplete an asset that can help pay for assisted living, if needed.
Which option is best for you? It is clearly a personal decision. If you have plenty of money saved for retirement, go ahead and get that house paid off. If you feel that you need to save more money for retirement, kids college, or other planned expenditures, just make your regular house payments and fill up your investment accounts.