Lets say my home's value appreciates considerably. How can I take advantage of this?
I'm unwilling to downgrade (all the other houses in my area has also appreciated, so if I sell and re-buy, I would end up with a smaller house).
Assuming "take advantage" means continue to build wealth, as opposed to blow it all on a fancy holiday...
Downgrade As you already note, you could downgrade/downsize. This could happen via moving to a smaller house in the same area, or moving to an area where the cost of buying is less.
HELOC Take out a Home Equity Line of Credit. You could use the line of credit to do home improvements further boosting the asset value (forced appreciation, assuming the appreciation to date is simply market based). Caution is required if the house has already appreciated "considerably" - you want to keep the home value within tolerance levels for the area. (Best not to have the only $300K house on a street of $190K-ers...)
Home Equity Loan Assuming you have built up equity in the house, you could leverage that equity to purchase another property. For most people this would form part of the jigsaw for getting the financing to purchase again.
There are basically two ways to get value out of an appreciating asset such as a home:
(a) Sell it and take the profit. In the case of a home, you presumably still have to live somewhere, so unless you buy a cheaper home to replace it, this doesn't get you anywhere. If you can get another house that is just as nice and in just as nice a location -- whatever you consider "nice" to be -- than this sounds like a winning option. If it means moving to a less desirable home, then you are getting the cash but losing the nice home. You'll have to decide if it's worth it.
(b) Use it as collateral for a loan. In this case, that means a second mortgage, home equity loan, or a home equity line of credit. But this can be dangerous. House prices are very volatile these days. If the value of the house falls, you could be stuck with debts greater than your assets. In my humble opinion, you should be very careful about doing this. Borrowing against your house to send the kids to college or pay for your spouse's life-saving operation may be reasonable. Borrowing against your house to go on a fancy vacation is almost surely a bad idea. The vacation will be over within a couple of weeks, but you could be paying off the debt for decades.
There might just not be anything useful for you to do with that 'value'. As others mentioned, HELOCs have their risks and issues too. There is no risk-less way to take advantage of the value (outside of selling)
It is similar to owning a rare stamp that is 'worth a million' - what good does it do you if you don't sell it? nothing. It is just a number on a sheet of paper, or even only on some people's minds.
Even selling isn't riskless. Sure, your house has gained value-- but unless that's due to improvements you made to it, every other house in the neighborhood you might buy has gained value too, so moving might not result in extracting any net value.
This is one of the reasons I keep reminding folks that a house is not an investment. It can be a business, if you're renting it out. But if you're occupying it, it is simply housing. If you are lucky you'll make a profit if and when you sell it, but don't count on that.
It does store value, but except for taking loans against that it's had to access that value. And lower loan rates than you'd otherwise pay are not a huge value when you'd save more if you don't borrow at all.
The only use I'm making of my house's value is that by taking a very-low-rate mortgage when I could have paid cash I was able to leave more money in my investments -- arguably the safest leveraged investment possible.