Lots of good answers here. I will specifically call out Bob Werner's as being the least so. Please don't think that his answer is based on much that's practical in most parts of the country. Good for him that he was able to do this (one assumes), but this theory is rather unrealistic in a mid- or high-COLA.
If a mortgage payment is about the same as rent in your area, it would take even more time to achieve home ownership via BW's plan than it would to buy with 20% down (yeah, save it up fast by being mustachian). At least you are paying toward home ownership rather than renting and trying to save towards an ever-receding goal. You can still be "super proud of yourself", even if you chose a different route to home ownership. Good luck to you!
I say all the following from a humble opinion of my own. I'm sure asking people to actually have the money to buy the things they want may rain on their parade. Everyone giving suggestions is welcome to share.
Of course MMM paid cash, so I guess I'm following his thinking. He also sold his house for just about what he paid for it after 7 or 8 years after riding out a significant downturn for a few years.
Would you borrow 80% to buy one single stock? I didn't think so. In fact, it is even illegal for brokerage firms to lend you money to do so. Would anyone here suggest borrowing 80% to buy a car because you wanted it and didn't have the money to buy it? I'm pretty sure the answer is no. But I see plenty of folks suggesting to borrow 80% to buy houses because people want them but don't have the money.
This site promotes stoicism in my opinion. Which is a nice way of saying -- "be a badass and if you "want" a house, actually have the cash to pay for it"
The reason that homes are expensive in high cost of living (COLA) areas is that they are overpriced. They weren't as expensive 4 or 5 years ago. If at that time you had suggested buying with 20% down it might have made sense. It may even make sense in the micro market where I live as home prices haven't moved much in the last several years and there are still plenty of foreclosures on the market.
The person who asked this question is probably renting a place now. If they want to upgrade they can simply rent a nicer house. They probably have it in their emotional heart that if they buy a house that somehow their life will be magically better than if they rent a similar home. I'm pretty sure it won't be. Driving a borrowed money 40,000 SUV doesn't significantly improve your life over a paid for 10K Honda Accord. Buying a house is not a "need." It is not a prerequisite for having a great and full life.
Oddly the more expensive the house the better the rent to own ratio tends to be. If you're looking at the top 20% of homes (which I actually do on a regular basis) the rent is often below what you would pay in interest, taxes, insurance and maintenance. (not in all cases or all markets) This appears true in Longmont, MMMs hometown.
Also, remember that in typical real estate cycles that the average house buyer only stays in the house for 7 years on average. (that's what MMM did). Your house is not a lifetime marriage by any means.
By the way, I have been dealing with houses, homes, real estate, renting and remodeling in one manner or another for over 30 years. I have seen many people lose all their assets on a house. I was a home builder when the real estate bubble bursts so perhaps I'm a bit skeptical. Sure for 90% of people it will probably work out buying a home they don't have the money to purchase. The hard part is knowing 5 years in advance if you're one of the 10% that it goes terribly wrong with. If you very confident you will always be in the 90% then by all means, save the 20% down and jump!
Regarding CATCCC's question about paying cash for a home or putting 20% down and investing the difference.
At these interest rates I would lean towards 20 down and invest the diff. The spread would be 5-6% over the long haul (30 Years). That would be a 5 million dollar difference on a 500K home. You're still gambling a little but the perfect storm risk of houses being way down, stocks being way down and you having to sell the house all at the same time is pretty low. (this did happen 5-6 years ago by the way) With each passing year as you save more the risk of the perfect storm diminishes to close to zero. So the gamble in this case is would you be willing to take on a very low risk for an additional 5 million dollars? And how good are you at evaluating risk and tolerating market swings?
But hey, don't listen to me!