Ok, I must confess, it sounds a lot like LastPass.
It's much more what lastpass wants to do, rather than what lastpass does, but it's all there.
Using lastpass, it will detect a sign-up page. It will allow you to auto-fill the page with the identity of your choice and generate a strong password. Once you're in it will detect the login pages and auto-fill your credentials. I believe you can set it to auto-login to certain sites too.
LastPass stores your credentials in the cloud, but encrypts them on your endpoint so that they're secure. It runs on almost any device, although the degree of integration is very limited on things like iphone and android, and is usually missing from within applications themselves (spotify, any phone app), which is annoying.
Remember, our web passwords are way beyond just websites now, don't forget our beloved mobile apps.
Are we asking for a version of lastpass that can be easily integrated with sites, browsers and apps, from both a practical and legal point of view? I guess we don't want to make a monopoly here, so it presumably couldn't be last pass explicitly.