I am in the "pay the minimum" on the mortgage camp. Invest in something else with a better return than the mortgage rate. Don't like the ups and downs of actual stocks? Look at closed ended funds with monthly dividends. My mortgage is cheaper than renting; eventually I will own the place outright. I do not look at it like a loss, just a cost of living.
The one thing you cannot buy for any amount of money is time. If you have the time, put the money where the time will work for you. Sure, you will lose some to mortgage interest but as many others posted above that money gets "cheaper" over time. That is precisely why mortgage lenders get proportionally more interest early in the mortgage term than later. The loan is designed to benefit the lender.
I made sure I had 20% in (required on my loan to avoid PMI and escrow) back when I started my mortgage. I paid up for a little while until I realized that it really was not buying me much shorter a loan term and in the short run I always had less money to invest or use for some other purpose. Invest your money in things that get returns; could be stocks, real estate, flipping cars for profit, whatever. Just remember that if the investment costs you more than you get out of it then it is a liability, not an asset. Most people have it wrong that the house they live in is an asset (and every real estate agent sells this falsehood as well). Typically most people's homes do not make them money, they cost them money (a liability) through taxes, upkeep, mortgages, etc. Even with it paid off it is still a liability. The home only makes money when it is sold or if you are renting out a portion of it for profit. It is not a bad thing, just is what it is.
Books I recommend for overall money strategies:
Rich Dad, Poor Dad
Automatic Millionaire
Millionaire Next Door
Richest Man In Babylon