For web sites I don't want to access from my phone, I use the PasswordMaker plugin for Firefox, which generates site specific passwords from a single master password that never gets saved anywhere (except maybe swap space, I haven't looked into that). The only problem I've run into were overzealous input sanitizers on some sites that refused some of the characters in the generated passwords.
For really important passwords I use strong random passwords with a security copy on paper stored in a safe place. Depending on the password and how often I need it that may be the safe at work, a binder with all the important related personal documents, or that place all people use to keep valuable small pieces of paper, the wallet in my pocket (there usually without a full domain name).
Then I use old safe passwords which I no longer use for their original purpose but still remember as passwords for situations where PasswordMaker is no option.
For really important passwords I use strong random passwords with a security copy on paper stored in a safe place. Depending on the password and how often I need it that may be the safe at work, a binder with all the important related personal documents, or that place all people use to keep valuable small pieces of paper, the wallet in my pocket (there usually without a full domain name).
Then I use old safe passwords which I no longer use for their original purpose but still remember as passwords for situations where PasswordMaker is no option.