Google will only know the leaked passwords, (and only the ones that they know). They don't even know your password that they use on their own site.
Some sites do know your password, you know which bank you are (I don't know why, but banks seem to be particularly bad at this). If they don't know to do password authentication without storing your password, then they are the sort of company that is also more likely to be hacker, or leave a USB-storage-device containing your password and other sensitive data on a train.
And if you get a phishing email, they are trying to invoke a behaviour in you, that will result in compromising your self. If they know your password, then they will not e-mail you saying we know that your password is abcxzy. They won't even tell you that they know it. If they know it, then they want you to be ignorant of this for as long as possible.
Therefore use a password safe/manager (User is already doing this). Use a different password for each site, use passwords of 30 random characters, unless forced to make it weaker by the (banks) security policy. And lock the safe with a good strong pass-phrase, using muli-round encryption (taking about 1/2 a second: fast-enough not to be a pain, and slow-enough to stop an attacker).