From Bitstamp.net:
ACCOUNT VERIFICATION
There are no transfer limits or trade limits for "verified" Bitstamp users. In the event that you would like to remove the 1000€ first time deposit limit on your unverified account or the 10,000€ deposit limit for any future deposits and/or withdrawals, verification is necessary.
To verify your account please submit a HIGH resolution image of a valid government issued ID (passport, ID card, driver's license,..) and of a recent utility bill (electrics bill, phone bill, rent contract,..) addressed to your name no older than 3 months from the day of the submission.
That means that you can deposit up to 1.000€ the first time and after that up to 10.000€. You can trade with an unverified account and I don't think that there are any restrictions besides deposits/withdrawals. My verification took half a day.