Have you tried KeePass or LastPass? They work pretty well on just about every platform.
Unfortunately, all three major browser vendors seem too busy pushing their own single sign-on schemes (Chrome: Google account, IE: Microsoft account, Mozilla: Persona). So they're unlikely to pay any attention to plain old password generation and storage for the foreseeable future. Which is a real pity because passwords aren't going to disappear overnight.
I've been using LastPass for a long time and even purchased their their Enterprise version for $work. I also use KeePass and recommend both.