Why does anyone expect people to remember?
Even a casual internet user would likely need passwords for PC logon, ISP, email. router admin, Wi-Fi, bank, building society, Amazon, eBay, gas and electricity on-line accounts, Facebook and Twitter, as well as non-internet PINs for credit and debit cards. It's just not reasonable to expect human beings to remember all these. Most people I know have their pssswords written down, or have simply forgotten the less frequently used ones.
The only practical answer is to use a password utility such as provided with some AV programs, or a stand-alone utility such as Keepass. For me it's an essential piece of software.
I avoid creating passwords wherever possible but even so I have 392 passwords ... of which probably 1/4 are defunct and I will never need about 3/4 of the rest (only I'm not quite sure which 3/4.) Some of these belong to relatives in case they ask me to sort out problems with their email etc.
But they're easily managed with Keepass, and available on my desktop PC, laptop and phone, by sharing the encrypted password file on DropBox.
I only have to remember the master phrase, and I use that often enough to remember easily. Should I change it regularly though? Surely it it's secure I don't need to, and if it isn't, by the time I change it, it would probably too late.