Since my degree is not in finance I will cite Trump here.. "If you owe the bank enough, you own the bank". Paying off your mort is a 1950's dream and has been the line of thinking for many years.
Due to the unstable job market and economic times, having that money tied up in equity in a home will not pay your hospital bills or braces for your kid when you loose your job or simply cannot get a loan due to our recent credit crunch. I am a firm believer that having those funds in an investment that can be accessed for emergencies is the best route to take. I remember getting laid off and needing to pull some of the equity out of my personal home, the banks said "No job, no loan"
After years of making an extra payment every so often, it didn't matter. They wanted their mortgage payment and since the home was worth far more then what I owed, they were all to happy to come and take the home. Luckily, I got another job and was able to fight them off and catch up with my mortgage.
Its a new world and trying to use the same financial concepts that were used in the 1950's may not work so well anymore.