That's an extremely broad question. Quarters have been issued since the 1790s so there are many valuable issues, and the "most valuable" title can shift as time passes. Some of the highest-value quarters are 1796, 1870-CC, and 1871-CC. You can find a full set of current prices at any number of web sites. One good portal site is http://www.coinclub.com/prices/
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 rarest and most valuable Morgan dollar is the 1893-S, with a mintage of only 100,000. Prices for this date start at about $2,000.
From least to greatest: Penny Nickel Dime Quarter Half Dollar Gold and Silver Dollar
The most valuable American coin in current production is the half dollar. This half dollar is worth 50 cents when used.
Quarter a dollar (1/4 a dollar)
I believe they are all worth 25 cents...
1922 is by far the most common date for Peace dollars. As of 13 April 2013, one is worth about $20 for the silver.
alibyan ten dollar note.
20 dollar bill
The most two most valuable are the 1903-O Morgan and 1928 Peace dollar, followed by the '21 Peace and the '02-S and '03-S Morgans.