It depends on the coin. If it is dated 1965 or later, unless it has some sort of interesting error or is a proof coin, it is only really worth face value. It might be worth about a dollar to a serious collector, but you will find a really hard time finding a buyer. If it is dated 1964 or before, it is 90% silver and worth at least $6 for the silver content alone. Depending on the date/mintmark, it may be worth more.
A 1937 Washington quarter is common, assuming it's circulated and has no mintmark values for coins in average circulated condition are $8.75-$9.50.
Retail is $3.22-$5.00 in average circulated condition
It's worth 25 cents. And it is not likely to be worth any more in our lifetimes.
Common date circulated silver quarters are worth about $2.75 each.
Value runs from $3.00 to $10.00 in average circulated condition.
A 1959 Washington quarter is very common. Circulated coins have retail values from $7.50 to $8.75.
If it is circulated it is worth $3.00 to $15.00. If it is uncirculated $30.00 to $50.00. Around 14,600,000 were made.
A coin in average circulated condition has a retail value of $7.00-$15.00.
July 2, 2009 A 1959 Washington Quarter in uncirculated condition sells for about $8-$12. In circulated condition it sells for about $3-$4.
With out a grade the best I can do is a very wide retail price range of $5.00 to about $300.00 in circulated condition.
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