There was something on a recent TV news program about this type of arrangement that worked out for some folks. The problem I see is that you are working with such a limited segment of the market (your finding just the right home and the other party finding your home to be just the right for them). Then there is a matter of the market value of your vs the market value of the other home. Who determines this? Will you be getting an appraisal? Also, the lender that holds your mortgage (if you have a mortgage) will have a "due on sale clause" which means that here will need to be a an exchange of funds to pay off your current mortgage. What about the other house...does that have a mortgage? There will probably be a "due on sale" clause on their home too. You really need professional assistance to do what you are asking. I would suggest contacting an attorney and a tax accountant to see if/how this will work for you.
The trade that I am most familiar with is called a 1031 Exchange and involves only investment property and everything is handled by a "Facilitator" a trained professional who does only Exchanges.
In my opinion, we are not in the type of market nor the market area for this to work the way you would like. Much success to you and I'd like to hear how it turns out.

Trading homes is more challenging than like say a car. You can take your car in and trade it at a dealer and they can sell to a potential buyer while holding onto the title. A deed can't be held in limbo while a buyer is found for the home. Do you owe anything on your home? If, so that would have to be paid off, unless it is assumable and the potential person you would want to trade would be wiling to assume the loan. The state will want their money like Sam was saying upon the transfer of ownership of the deed. The real challenge is you would have to find the right house for you and the other person would have to be a great match for your home. It is a great thought to be able to trade, I have been asked that questions by my clients over the past 20 years and in the end have sold their home and found them another one to purchase. The current real estate market is in a slow transition from a fantastic buyers market to becoming more stable. There are some great buys on homes still out there, however they are selling faster and the number of great buys are going down. The interest rates are fantastic and are hovering in the low 4 percent.

Steve R Halvorson
425-754-3010

The first thing that comes to mind is Craigslist. I believe I have seen ads like this on Craigslist. Word of mouth, networking, investor groups are others that may have possible opportunities.

"Trading" is not as easy as it sounds. Most likely you will still pay an excise tax to the county (about 2% of the home's value), and may owe other fees. You need to consult a tax advisor to go over the details of the transaction you're attempting, as it may be more involved than you think.