Would double spending be illegal under US law? If bitcoin is classed as a currency would it be considered forgery?
Illegal? No. Bitcoins aren't recognized as "currency" so there is no US law governing their use. You could claim fraud, but fraud requires someone to be harmed, no one is harmed when a coin is double spent. You still got your coin, it's just that he didn't lose it. Welcome to digital currencies.
If bitcoin were classified by the US Government as a currency, then maybe forging the block chain and validating double spends would be counterfeiting.
We're a LONG way from any of the above being law. And that would only be a US law.