Incorrect. I use Lastpass exclusively. It syncs across all your devices.

It generates arbitrary-length random passwords (things like fjFJ38f;dnep0S_) and stores them encrypted on LastPass's servers. They never see your password; all encryption/decryption is done on your computer. There are browser plugins for Chrome, IE, and Firefox, and there are apps for iOS and Android. It syncs your passwords across all your devices, will auto-fill login forms, and makes it about as easy as possible to have a different random password for every site.

It even supports two-factor auth, one time passwords, and other fun things for the truly paranoid (like me).

CHeck it out!