What is the value of a 1901 US quarter?

These coins are usually called Barber quarters, after their designer Charles Barber. Look on the back of the coin to see if there's a small mint mark letter below the eagle. It may be blank or there may be an O or S.

Numismedia lists the following approximate retail values as of 10/2011:

No mint mark (Philadelphia):

Very worn condition - $10

Moderately worn - $22

Slightly worn - $32

Almost no wear - $125

Uncirculated - $210 to $11,250 depending on quality

"O" mint mark (New Orleans):

Very worn - $36

Moderately worn - $150

Slightly worn - $240

Almost no wear - $734

Uncirculated - $960 to $33,150

"S" mint mark (San Francisco):

Very worn - $4,770

Moderately worn - $16,200

Slightly worn - $19,800

Almost no wear - $29,964

Uncirculated - $35,400 to $182,000

Any suspected "S" mint coin should be examined by a professional to make sure it's not a fake.

DISCLAIMER: The retail values quoted are the best available as of the date shown, but may vary significantly due to changes in the precious metals market. Also the wholesale (buying) price of a coin will be less than the selling (retail) price. A reputable coin dealer will be able to give a more accurate valuation based on inspection of the coin.