Never knew of the ability to give your private key on MtGox. Seems like a ridiculous method of deposit unless they immediately moved the coins to an address that they fully controlled. And only verified the funds once those coins had moved.
You do not own coins unless you (and only you) have the private key.
web wallets are nice for the convenience, but never leave as much as your willing to lose overnight in them. I agree with the above post I started out leaving all of my btc in a webwallet, but I have recently moved everything but a few dollars into paper wallets in encrypted files. the most important thing to remember is you need to know your private key, otherwise it is not your bitcoin.