I could argue both sides.
BUT....one of the best feelings you will have in life is when you pay off your mortgage.
Three years ago, I sold off two pins for around $10k because I was in such striking distance of getting out from Wells Fargo, and it felt great.
A word of caution, banks do everything withing their legal power to stop you from making those last payments. Its a separate department (it was for Wells Fargo) and even when I tried to walk into a local office to make a final payment, they turned me away.
I would do it again in a heartbeat....even though its probably not financially the most prudent thing to do.