Publication 551 doesn't appear to address household goods, but land and stock.
This link addresses goods, and says they must be in good condition (fair enough):
http://www.irs.gov/publications/p526/ar02.html#en_US_2013_publink1000229705 "Used clothing. The fair market value of used clothing and other personal items is usually far less than the price you paid for them. There are no fixed formulas or methods for finding the value of items of clothing.
You should claim as the value the price that buyers of used items actually pay in used clothing stores, such as consignment or thrift shops."
That seems pretty straightfoward--if a good-condition pair of pants sells for $5 in the thrift shop, you can claim $5 for it. But I don't think the above needs to be interpreted as
you had to pay for them, only that the price is far less than the buyer paid for them.
However, for household items, not having a receipt could be a problem:
"Household items. The fair market value of used household items, such as furniture, appliances, and linens, is usually much lower than the price paid when new. These items may have little or no market value because they are in a worn condition, out of style, or no longer useful. For these reasons, formulas (such as using a percentage of the cost to buy a new replacement item) are not acceptable in determining value. You should support your valuation with photographs, canceled checks, receipts from your purchase of the items, or other evidence. Magazine or newspaper articles and photographs that describe the items and statements by the recipients of the items are also useful."
But arguably, the value of a used household item is what the thrift store can sell it for.... So what goes with clothing probably should go here.
I'm not seeing anything here that prohibits you from getting a tax-deduction on items you received as a gift (which is what you're getting from your neighbor :), just that you have to be very practical about basing its value on thrift-store resale values, and that it has to be in "good condition" i.e., working, usable, and resalable.