Paying off your house is an emotional decision. I don't mean that as a criticism because risk tolerance varies from one person to the next. However, this is Ramsey's target market - selling by emotion is a great strategy, so this isn't a criticism of Ramsey in that regard. He is very successful.
For those people that are inclined to pay off their mortgage, something to try that will benefit you. Limit your house payoff to 10%, or 25%, or 50% of your monthly savings (get a little feel good with your mortgage paydown, but still use logic to overcome that emotion) and keep your home equity lower than 25% of your total net worth (and that is on the high side to allow for some "feel good").