The worst is websites which not only disable pasting but don't even let you type your password in. Instead you have to use their janky on-screen keyboard to fumble your way through login. I got so fed up with TradeKing (which has horrible security practices in general) that I close my account.
HSBC has this really odd system where they only ask for the (e.g.) 1st, 6th, and 7th characters of your password. That implies that they store plaintext or something reversible...
To be fair, they're right in the middle of rolling out a new banking site which I think has proper passwords. The current system is a holdover from when they only had phone banking.