Mortgage rates are at record lows. The 30 yr fixed is now below 4%, if you are in the 25% bracket and itemize (state income tax, property tax, donations, easy to pass the minimum) it costs you 3% post tax. This is the rate of long term inflation, effectively making this money free.
You are likely to be able to average a far greater return than this mortgage is costing you. These rates may last another year or two, but long term, they are an anomaly.
ETFs such as DVY (the Dow high dividend stocks) are yielding over 3.75%, 3.2% after the 15% cap gain tax. i.e. you get a small positive return, and the potential for capital gains. If this ETF rises just 3%/yr it's all profit above your cost of money.
That said, there are those who sleep better with a paid in full house, regardless of the rate. To that extreme, I've read those who make paying their mortgage a priority ahead of funding their matched 401(k). While I can guess what the market will return, but can't know what will actual happen, it's foolish to skip one's match. They reason that the market can crash, I reply the 401(k) has to have a short term fund, money market or T-bill type returns, but a 100% match is a no-brainer.
Using an estimated 4% for the 30 and 3.5% for the 15, the payment on the 15 yr mortgage will be 50% higher, $1430 (15yr) for $200K vs $955 for the 30. How does this play in your budget? Do you have an adequate emergency fund? Are you funding your retirement plan at a decent level?
In the end, there is no right answer, just what's right for you. Understanding the rest of your financial picture will get you more detailed advice. Not knowing your situation limits the answers.
Edit 6/30/2015 - When I wrote this answer, the DVY was trading at $48.24. $100,000 invested would have given off $3187/yr after a 15% dividend tax rate. At $75/share now, the $100,000 investment would be worth $155,472 and yielding $5597 for a net $4757 after tax. The choice to go DVY would have been profitable from the start, with room now for a 35% crash before losing any money.