I take a tiered approach: I use Chrome's password manager for things I don't care all that much about. I use PasswordSafe in a shared file in cloud storage for passwords that I care a bit more about. And for those very few that are incredibly important to me, I just memorize the password that's usually made up of some long nonsense phrase (e.g. "apple youth brandish frobnitzer brainiac") which has enough obscure words to necessitate a very hefty dictionary to crack (or even a made up word or two).
Of course, I also have to memorize my Google and PasswordSafe passwords, since writing those down would compromise the first two storage systems.