The U.S. Mint struck the first silver half dollar in 1794 with the "flowing hair" Liberty design and minted its last primarily silver half dollar in 1964 as part of the Kennedy design. The two centuries in between represent billions of coins and several different designs, most of which are highly prized by numismatists. You should consider several factors as you determine the value of your coins.
Find a reputable price guide. One of the best print copies is "Whitman's Red Book," which provides color pictures and examples of rare and error coins. Also try bestcoin.com, which has an extensive price guide.
Determine the grade of the coin. Coins tend to grade between good (G-3) and gem uncirculated (MS-65), with the latter being extremely hard to find and fetching premium prices. Grades will vary by coin, so check the price guides for guidance. Generally, for a coin to grade in an uncirculated condition, it must have no wear and few contact marks, along with a nice luster.
Check the mintmark of the coin. Silver half dollars were minted in several different locations over the years, in such cities as Philadelphia, San Francisco and New Orleans. Some mint locations struck fewer coins than others during certain years and coins with that city's mintmark can sell for more. For example, only about 55,000 copies of the 1870 half dollar were minted in Carson City, Nevada. Most half dollars from that year would sell for about $25 in good condition as of 2010, while those with the "CC" mintmark might sell for close to $1,000.
Look for rare error coins. Mistakes occasionally occur during the minting process. The 1844 New Orleans half dollar, for instance, features the date stamped twice on some of the coins struck there. Examples of this coin can sell for more than $1,000 in fair condition as of 2010, or about 20 times what a non-error coin might fetch.