Should you pay down your mortgage?
I'm assuming that an emergency fund and an appropriate cushion of savings is built up. If it isn't, you need to work on that first before considering whether to pay down your house.
First, if the market crashed (again), and you lost your job, could you afford to sell the house and move to where the jobs are? Basically, if you put less than 20% down, particularly if you have private mortgage insurance, paying down the mortgage is a good idea. It frees you to move when you need to, so if the local economy tanks, you don't have to go down with the ship. Also, extra payments early in the life of the loan save a lot more interest than investments later on.
Second, what does your investment portfolio look like? A house is a highly-leveraged, sector-specific, non-diversified investment. If you sank half your net worth into tech stocks, people would think you were crazy. If you borrowed several times that amount and invested it as well, they'd say you were crazy. If you bought all that stock in a single tech company, they'd know you were crazy. Yet if you do the same thing with a house, no one would bat an eyelash. If you're well and thoroughly invested in the rest of the market and you want to increase your exposure to real estate, paying down your mortgage is a reasonable decision.
Third, I've deliberately ignored comparisons of rate of return, investment risk, inflation risk, and other such considerations. Don't worry about the details until you've got the big picture. One thing that I would add, however, is that even when you take all of those into account, remember that the money you've locked up in equity is in there until you sell the house or pay off the loan, which could be a VERY long time. And if you sell during a downturn, you may not recoup the money at all. Which leads to my next point:
Fourth, the return on investment is heavily back-loaded. You don't see any improvement in cash flow until you sell the house (assuming you make a profit) or pay off the mortgage. The time value of money is a definite consideration. A $1,200 mortgage payment is worth a lot more now than it will be 20 years from now. So if you're at the point where you could be free of your mortgage in short order, and create a large cash flow, it may be worth it, but then you're not really saving all that much in interest if you're in the last few years of the mortgage.
With that being said, if you want to increase your investment in real estate, I would recommend investing in energy efficient home improvements. Increased energy efficiency has an immediate, after-tax, inflation-adjusted cash flow, shields you from fluctuations in the energy market, and increases the value of your home which provides additional equity to get you above the 20% line.