What is the value of an 1842 US half dime?

Depending on condition and mint, assuring it is not a common replica. A seated liberty half dime would fetch anywhere from $10 - $250

UpdatedLook on the back of the coin to see if there's a small mint mark letter. It may be blank or there may be an O.

Numismedia lists the following approximate retail values as of 09/2010:

No mint mark (Philadelphia):

Very worn condition - $14

Moderately worn - $20

Slightly worn - $25

Almost no wear - $112

Uncirculated - $156 to $2,500 depending on quality

"O" mint mark (New Orleans):

Very worn - $28

Moderately worn - $75

Slightly worn - $201

Almost no wear - $1,134

Uncirculated - $2,000 to $15,940

DISCLAIMER: The values quoted are the best available, but may vary due to market fluctuations. 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.