1. Create a complex password to re-use everywhere. Memorize it and don't write it down.
2. Create individual simple passwords when you need one. Write them down
3. Create a method to combine the complex password and the simple password. Memorize it and don't write it down.
I figure there are two main attack vectors: online and offline. Online attack vectors are either a dictionary attack, which requirement 1 solves with a complex password, or using hacked passwords in one site to gain access to other sites, which requirement 2 solves with different passwords for each site. Offline attack vectors are someone discovering your written passwords, which requirements 1 and 3 solve by memorizing pieces of it.
The only weakness to this scheme is if someone is A. deliberately targeting you as opposed to a mass attack, and B. gains access to two or more of your passwords, allowing them to figure out your password system.