Again if you have RussianPolandSweden on one site and LightTacoMadness on another site, than it's not so hard to figure XxxxXxxxXxxx on the third site. It's even easier if it's machine generated. Passwords RussianPolandSweeden on facebook and LightTacoMadeness on gmail may not throw any light on their similarities and systematic formula for you, but it will definitely mean something for other people. And yes, It's very hard and almost impossible with one password, unless you get to unveil relation between password and site, but having two or even more passwords makes it very easy for cryptologists.

Even though I did overrate middle class Russian cryptologists, look at this from this point of view, A is your site, B is your password, C, D, E, F, etc. are any additional sites, and C1,D1,E1,F1 are any additional passwords available. We have a formula (A:B) = (C:X) (where "x" is unknown) with a single password, very hard, but not impossible to find any additional password , and (A:B) = (C:C1) = (D:X)(where "x" is unknown) with 2 passwords available, makes it relatively easy task to do. Because A to B is parity to C to C1 and is parity to D to X.

And the only way not to get all your passwords unveiled is to generate them randomly with random characters, but you already mentioned in one of your early messages, that system is used.