What is the value of a two-headed US quarter?
They are novelty coins, manufactured for the novelty or illusionist/magician's industry. They're made by altering two normal coins and gluing the pieces back together. If you use a strong magnifier, you can probably find a seam just inside the raised rim on one side of the coin, or around the edge. Technically, they don't have any value except when someone wants one and is willing to pay for it. You can buy them in novelty shops for about $8, or on eBay for $2-$3. Sometimes people will spend their two headed coin without remembering that it isn't a real quarter. One WikiAnswers user claims to have made to a coin collection place in Detroit who said they had a real one that is selling for $100,000, if it is authentic. Sadly, no two-headed quarter has ever been certified as an authentic mint error, though one two-tailed quarter has been certified as an authentic mint error. This means that, in theory, a two-headed quarter with the same date on both sides could be authenticated, but the chances are more in favor of it being the manufactured novelty/magician's coin. Unless it's a genuine mistake that occurred in the mint, it's probably worth a few bucks at most. Two-headed quarters are often sold in magic and gag gift shops. See the Related Links for more info about these coins.
By far, the most valuable quarter is the 1916 Standing Liberty Quarter Dollar - its value in good condition (G4) is: $3000. places the value of the 1916 Quarter at $3900 in G4 and $35,000 in MS66 (but look fast, it may be higher by the time I finish typing this). The first US quarter from 1796 is listed at $12,000 and $400,000 in those grades.
The Mint has never made gold quarters. If you have a gold quarter then it has been plated which destroys the numismatic value of the coin. Its value is 25 cents plus the value of the little bit of gold they used to plate it. Some chemicals can cause the quarter to turn different colors. This also does not enhance the value of the coin.