Quoted:
Quoted: Don't apply any extra prinicpal to your mortgage if it's under 8%. Invest the money instead. 
Mathematically I'm not sure I see that. Intuitively, I would really like to not have a mortgage when I retire.
If I pay an extra $250 towards the mortgage, I'd have it payed off in 21 years and 2 months (the year I retire), leaving me about $1,500 less in monthly payments and full equity in the house.
If I invest that $250 at 8% instead, I'd have earned $102,868 (total $166,386 p+i) after 21 years and 2 months but still have $119,157 left on the mortgage. After the 21 years, I will not be earning enough on that investment to cover the remaining monthly mortgage payments, so isn't that a losing proposition? If after 21 years, I have earned $102,868 in return but still have a $119,157 debt, isn't that a loss?
Am I missing something obvious?

Well, lets do a oversimplified test:
Option 1:$97,100 mortgage, 8% interest, 30 year fixed. Payment of $712 a month.
I take $250/month in an
imaginary money market account, guaranteed to make 8% interest over the long term. I save for 14 years. This accrues to $77,000 after 14 years.
After 14 years, the outstanding balance on my home is $77,000.
I now have the option to take the cash, and pay off the 30 year note in just 14 years.
Option 2:$97,100 mortgage, 8% interest, 30 year fixed. Payment of $712 a month.
I take $250/month and add it to the payment as extra principal.
Home is payed off in exactly (yeah, you guessed it) 14 years. Interest compounds the same in either direction. It is simple math.
Here are some things to consider:
1. The above example is oversimplified. In option 1, As you earn interest on the $250 savings, you will be taxed on this interest annually as income. This is slightly offset in option 2, as you pay extra on a home, you reduce outstanding principal quickly, and therefore reduce your tax benefit of the interest deduction. This is likely a wash, but you would have to run these exact numbers, with assumptions on tax rates in both directions. Lets leave it out for the sake of discussion, as it really isnt all that significant.
2. There is NO guarantee that you can make 8% interest to match the cost of interest on the home. The stock market does earn around 9% over the long haul, but there are no guarantees, and a loss of principal savings at the wrong time could wreck your plan. Safe equity investments earn from 3 to 6% over the long haul.
3. If you pay extra on the home, you *know* exactly where your money is going. Some people cannot save cash over a long haul, they will be tempted to invest it elsewhere, make purchases, etc... and then the whole equity offset plan is ruined. Personality plays a BIG role in these decisions. Know thyself.
4. This is a different equation than saying "I have this $100,000 in cash TODAY. Should I invest it, or just pay cash for my home and save all that interest?" The numbers there have to be evaluated differently.
So  overall, should you pay extra on the house, or invest the money? That is still a question that must be answered by every individual, their habits, discipline, and risk tolerance.
For instance  my mortgage is 5.75%. Money market accounts are easily available that grow at 5% *right now*. For me  I would rather save the cash than pay on the house. The growth rates are similar, and for now, with interest rates rising  my outlook is great.
Cash gives you options. Cash gives you power to make decisions. Cash lets you pay off your home, or use the money for an emergency elswhere. If the value of the dollar crashes... but your cash is hedged against a fixed rate home mortgage, your cash hasn't lot a CENT of it's value, in my opinion. No different than sitting in cash or sitting in equity.
However, if and when the market rates fall again... and you can only get 2% in a safe investment  that might be the time to convert that cash and pay down your mortgage.
These situations are different for everyone. Most people should pay down their mortgages... because most people lack the discipline, or interest, to play this money game along the margins. If you have the means and will to live mostly debt free, and not check to check.... then you are already way ahead of most people.