What is the value of an 1807 US dime?

You should have your coin authenticated by an expert. Numismedia lists the following approximate retail values as of 09/2013:

Very worn condition - $640

Moderately worn - $1,180

Slightly worn - $1,380

Almost no wear - $4,026

Uncirculated - $6,220 to $20,630 depending on quality

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.