That may sound like a stupid idea, and many years lots of security-minded people tried to educate users not to do that. But I think they have a point. Someone who uses the Internet regularly accumulates a whole bunch of accounts and passwords for all sorts of sites, servers etc. It's simply too hard to remember all of them. Thus far I agree.
But, I don't think writing down passwords on small pieces of paper and carrying those around in your wallet is a particularly good idea. It happens too easy that you lose your wallet, it gets stolen, or you lose the pieces of paper. Not to mention all kinds of social engineering activities, which are simplified a lot by this approach...
I do propose to write your passwords down. But do it in a computer file on a box where you're the only one with an account (your home PC or laptop). Encrypt that file with GnuPG and your're reasonably safe. Every time you need a password, decrypt the file, read and use the password, then wipe the decrypted plain-text file.
No more pieces of paper - help save the environment.