The safest (if craziest) way to store them is to memorize them all.
Now that so many people are working from home, outside the office intranet, the number of passwords you need may have significantly increased. The problem is, most of us don't know what makes a good password and aren't able to remember hundreds of them anyway. For seven years running that's been '123456' and 'password'-the two most commonly used passwords on the web.
We know they're good for us, but most of us are happier snacking on the password equivalent of junk food. Password managers are the vegetables of the internet.