Your equity was always imaginary
You used to hear the term "land rich, cash poor" for people who owned valuable land but didn't have quite enough money to make ends meet. It's an expression that dates back to the days when property was the only kind of real wealth there was. It's kind of fallen out of fashion of late. But as property values keep falling, it's worth thinking about the ways in which land is wealth.
In those days, land was wealth because it produced income--crops, grazing, timber, game, etc. If the land didn't produce an income, it wouldn't be considered especially valuable (so, the owner wouldn't really be land rich), but it was possible to ruin the income from your land through poor management or bad luck. That was how you found yourself land rich but cash poor.
The only sort of land ownership that most people have any involvement with nowadays is home ownership. Ordinary urban and suburban plots don't tend to be particularly productive (although you can grow a garden on one, and actually produce quite a bit), but there's a second way in which land can be valuable: You can rent it out. Or--and this is really the same thing--owning a home makes it unnecessary for you to rent one.
Economists use this logic all the time--not having to spend money is equivalent to receiving the same amount. This economic logic is correct, although you have to take care not to fool yourself about what expense you're really avoiding, as in the old joke:
This guy gets home from work really late. When his wife asks why, he explains that he decided save 50 cents by walking home instead of taking the bus. His wife says, "Idiot! If you were going to do that, you should have saved $5 by walking home instead of taking a cab!"
This, then is another way of valuing a home--it's worth whatever you'd have to pay to rent an equivalent place to live. (Of course, you need to adjust for any difference in expenses--taxes, maintenance, insurance, water, sewer, garbage, etc.)
We've mentioned two ways to value land: its productive value and its rental value. The third way to value land at its market value.
Market value, of course, is the most common way to value anything. It doesn't work very well for land for various reasons: each piece of land is different, most pieces change hands very rarely, owners will resist selling if the sale price won't cover the mortgage, etc. (It's because of all these problems that we even have such a thing as "appraisers.")
Along with all these problems with valuing land by its market value, the worst thing is that it's prone to lead you to imagine that the "market value" minus what you owe on your mortgage is your "equity."
In It Doesn't Matter What My House Is Worth, paidtwice talks about the difference between equity that's produced by paying down the mortgage versus the equity that appears out of nothing if the market values of the house goes up. She makes a good point, which is that if house prices in general are rising, then you can't translate that latter equity into an improved standard of living: If you sell and move, your new house is just as overpriced as your old one was; you don't come out ahead.
The fact is, though, that your equity is imaginary whether it's produced by soaring property values or by paying off the mortgage. Unless you're going to sell it, your property's only real value is what it can produce, plus what you can rent it for (or save by not having to rent someplace else).
This has always been true. Hopefully, it'll be a little more obvious going forward. Confusion about real value is what leads to bubbles and crashes. When only a few people get confused, they're mostly the people who suffer the consequences. When you get the sort of mass confusion we've had over the past few years, though, popping the bubble leads to bad consequences for lots of other people as well.
I think we'll know we're clear of these economic troubles when expressions like "land rich but cash poor" make sense again. It'll mean that people are valuing land by what it's really worth.