I memorize my key passwords. The rest are kept in a paper notebook stored in an unknown location.
You can make up memorable passwords that are secure by using mnemonic devices or simple substitution. For example: Password becomes P@$$W0rd.
If you want to memorize a series of passwords, use this approach and then create a mnemonic series based on the first letter of the passwords, such as Every Good Boy Does Fine where EGBDF stand for E@ch, G0od0ne, B0xer, D0gm@, F1e$ty, etc. You get the idea.
I've known some to use patterns on the keyboard. Just don't make it too simple a pattern or it will be compromised in no time.
Quis custodiet ipsos custodes? - Juvenal