The only password I need to write on a paper near my computer is of a client that require periodic change over his Vpnssl every 1 month. When connecting to it I must type it 3 different time in a context where password manager don't work.

After a year of trying to keep track of the changes via a secured method (and at least 12 call to their IT so they reset the password without any identity check on their part) I finally resigned and write it down on paper and write the new one every time they ask me to change.

Bonus fun fact : Theses idiots also truncated password at 8 characters but truncated in different manners on the 3 login steps required so it's only after 4-5 failed attempts at a secured corectbatterystapplehorse that I understood that weak password was mandatory by their rules...

PS: And of cour rotation between Passwd1 passwd2 passwd3 passwd4 (then back to 1) was perfectly accepted and considered as safe

I ended up memorizing my home's old WEP key simply because, since I was the "tech guy" in the family, everyone would ask me whenever they needed to add a device (never mind that I was mostly just going to the password booklet and reading it out). Eventually I just stopped needing to look it up. I've since used it in some places, blended with a mnemonic for the specific site. 10 hex characters plus a string might not be the highest-security thing, but at least it's not going to fall to anything less than brute-force.