Password managers are the only way to go. I have over 200 unique passwords for all the sites that needed registration over the last 15 years, each one is different. If one site is hacked then that is the only password the hackers get, it won't work anywhere else. The Copy/Paste feature means there is never any typos either.
I use the free Keypass2Android and the free KeyPass 2 on my PC. The password safe is automatically updated and saved in the cloud so all my old and new passwords are available wherever I go.
All the names and passwords can also be printed out with Keypass2 if you prefer to carry a paper list, make sure to write your name, address, phone, and email on the papers so they can be returned if you loose them.