From 1965 to 1969 US half dollars were struck in "debased" silver. The outer layer is 80% silver bonded to a core that's mostly copper, for an overall content of about 40%.
Unless the coin is in uncirculated condition or is from a so-called Special Mint Set, it's basically worth its metal content, about $2.75 to $3.00 as of 01/2010.
Note that from 1965 to 1967, US coins didn't have mint marks and proof sets weren't made so these details don't apply to a 1966 half dollar.
1970 halves were also made of 40% silver but were only sold in special collectors' sets.
All circulation-strike halves dated 1971 and later don't contain any silver at all. They're made of copper-nickel like dimes and quarters. Any that you find in change are only worth 50 cents, regardless of many myths and urban legends to the contrary.