Nothing wrong with writing them down, but put them on paper and keep them in your wallet or a safe. We put our SSN cards, driver licenses and passports and credit cards in our wallets. Why not our passwords?
If you are really serious about passwords, then generate random passwords offline on non-networked computers. There's an app called launch codes I use to do that. It uses random data from MS CryptoAPI to seed a Mersenne twister RNG. Letting people create their own password is like letting a child run with a knife in his hand.