I think for most of the major exchanges like Coinbase, Bitstamp, Bitfinex, Kraken, etc you have to be verified somehow either by your bank or other documents, before you can actively trade.
If you want to trade with minimal verification probably BTC-E or Cryptsy will do.
I am not an user of those big exchanges but as far as my experience goes with my local EU exchange I can trade without authentication as much as I am under certain threshold - for example: I can freely seling bitcoin until I reach 300 euro in transactions.