My last remaining brain cell is very soggy and regularly dumps information other than how to breath and keep my heart beating!
Seriously, with so many passwords and usernames floating around I found it increasingly difficult to keep track - not helped by the phenomina described by Jhieminga. I keep the problem in check by keeping a list of usernames, with the password listed as 'usual' - I only have one password that bears no resemblance or connection to me, my family, my career, job, etc. In other words, no-one in a million years could ever guess it by knowledge of me or my background. Same goes for PIN numbers - it saves ever having to write it down anywhere.
As for the PC problem, I experience the same frustration - some sites remember and some don't. It's an irritation having to type one or the other or both in to login to the site. I don't have an answer, I'm afraid.