A common myth about remembering passwords is that they should never be written down. This is patently false. In fact, you are far less likely to be compromised by physical access. And frankly, if someone does have physical access to your computer, it doesn't really matter whether you've written down your passwords or not - you've already lost the security battle.
Of course, this doesn't mean the passwords should be jotted on a sticky note and stuck to the monitor or under the keyboard. That's a definite no-no. Instead, keep the password reminder list in a locked file cabinet, safe box, or similar secure container.
You can even maintain the list on the computer itself, provided the file containing the passwords is encrypted with a strong password itself. And by creating passwords based on a category system, you've eased the need to revisit the list constantly.
Plain old memorizing is a good approach too. The mental exercise may just give your brain the workout it needs to stay younger longer.
Also see: Tips for Keeping Passwords Safe