Financial guru Clark Howard always answers yes to this question. He argues that there's a multitude of burdens that are lifted from any homeowner once the mortgage is paid off, some financial, and some mental. He cites documented increased happiness among retirees that have paid off or dramatically decreased their mortgages. The main break here is that it seriously reduces the amount of monthly bills you have to pay, and so you either need less income, or you get more net income after your overhead.
On the other hand, CNBC cautions against doing it automatically without considering several other factors. First, if you borrow for a long time at a low rate, your extra money might actually earn more through investments than you would save by paying off faster. Second, make sure the mortgage is a good one; if you bought too much home, you might have too much mortgage, and a good counter is investing for growth. Finally, are the monthly payments fixed? If inflation kicks in, then mortgage payments in thirty years might be the same as a utility bill, and there's nothing the bank can do about it if all payments are on time.