Are there bitcoin exchanges that do not require an extensive verification process? Are there bitcoin exchanges that do not require an extensive verification process to begin trading? I do not want to submit forms on MtGox.
No U.S. exchange. Btc-e does not but they will not do business with U.S. banks. Coinbase does not have an extensive verification process, but they are technically not an exchange, and to buy or sell bitcoins through their service you have to link a U.S. bank account which for all intents and purposes is the same thing as verification. 

Due to the patriot act any currency exchange doing business with the U.S. has the burden of proving that they are not laundering money for terrorists.