What is the value of an 1807 US half dollar?

You should have your coin examined in person by a knowledgeable dealer or appraiser to make sure it's genuine.

There are 3 major varieties of 1807 half dollars. Numismedia lists the following approximate retail values as of 07/2013:

Heraldic eagle type:

Very worn condition - $204

Moderately worn - $402

Slightly worn - $700

Almost no wear - $4,560

Uncirculated - $9,060 to $99,380 depending on quality

Bust type, small stars:

Very worn condition - $138

Moderately worn - $510

Slightly worn - $1,140

Almost no wear - $5,554

Uncirculated - $8,750 to $112,500 depending on quality

Bust type, large stars:

Very worn - $121

Moderately worn - $342

Slightly worn - $650

Almost no wear - $4,340

Uncirculated - $8,440 to $106,250

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.