You think the rarest would be when they made some of the first US quarters in our history.
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They're many facts about US quarters but ine is that all quarters made before 1965 contain 90% silver.
The US Mint in Philadelphia struck .............613,792,000 quarters in 1990. The US Mint in Denver struck .....................927,638,181 quarters in 1990. The US Mint in San Francisco struck ...............3,299,559 proof quarters in 1990. Total number of quarters struck in 1990: ..930,938,353
Certainly the single rarest US quarter is an 1866 proof version - only one of these was struck, and it's impossible to put a value on it. The quarter with the highest market value is a 1795 Draped Bust variety with a small eagle on the back. As of 02/2011 a top-quality one is priced around $450,000. Several other quarters fall in the $250,000-$550,000 range, including 1805 and 1873-CC.
1964 was the last year US quarters were made of Silver.
Do you mean rarest in terms of the number of coins issued, or in terms of values? Quarters have been issued for over 200 years and there are some enormously valuable specimens, including overdates and early proofs. You can scan a list of prices by looking at http://www.numismedia.com/fmv/prices/bstqtr/pricesgd.shtml and http://www.numismedia.com/fmv/prices/setqtr/pricesgd.shtml, for example. Assuming you are referring to Washington quarters, the rarest and most valuable are the 1932-D and 1932-S