Now there are software "password managers," such as Dashlane. I am not singling them out for any specific reason; they just happened to come to my notice through a friend's Facebook posting. I expect any day now to see a news item that Dashlane's password manager software has been hacked, due to an unnoticed security defect. That will be followed by yet another surge of identity theft and bank account draining.
Let me make this real clear: NO SOFTWARE IS SAFE. The INTERNET IS NOT SAFE. (Take that, cloud vendors).
If you feel compelled to keep a digital list of your passwords, put them into a Word or Excel document, store that in a USB stick, and keep it in a safety deposit box (seriously). Or, write them on paper and put that in the box. And if that sounds paranoid, just Google "bank and retailer accounts stolen." If major corporations can't keep their data safe, what makes you think you can?