Earlier quoted context omitted.
This is pretty brilliant. My biggest concern is that if my password for a site gets compromised, it gets a lot more complicated. Presumably I'd have to memorize a separate master password for retrieving the new password for that site.
They have a counter option that you can increment which allows you to generate a completely different password for the same site.
There is still the benefit that the passwords can't be exposed by a compromise of the service. Presumably it doesn't store your master password anywhere, so all they'd get is the site and counter info.