I wonder how gox hack is correlated to the password security. 
It isn't. I didn't trust it from the beginning.
coinbase.com? the site is live and working fine! What had happened?
Some coinbase accounts were hacked.
But most thought their account was hacked or something after they received a request (see http://www.reddit.com/r/Bitcoin/comments/21wyl3/coinbase_has_not_been_hacked_this_is_a_feature/)
NewLiberty is correct
My email address cannot be hacked using forgot my password. (even i don't remember that)
Can you tell me how did you deactivated it? Almost all the email accounts can be hacked using forgot my password, and this route is the most preferred one used by hackers to steal coins from BTC-E and other exchanges.
Just don't forget the password
