What is the value of an 1874 US quarter?

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 S.

Numismedia lists the following approximate retail values as of 02/2015:

No mint mark (Philadelphia):

Very worn condition - $23

Moderately worn - $40

Slightly worn - $96

Almost no wear - $482

Uncirculated - $900 to $20,310 depending on quality

"S" mint mark (San Francisco):

Very worn - $24

Moderately worn - $60

Slightly worn - $168

Almost no wear - $546

Uncirculated - $1,040 to $21,450

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.