Password managers can make and keep track of very secure passwords, and can employ very strong encryption to store those passwords. But on the other hand, you're putting all your eggs in one basket, so if it does get hacked, all your accounts could be exposed. Also, you can never be absolutely sure that the software itself has not been compromised. The chance of that may be very small, but it is never zero.
If you're paranoid about keeping your most critical passwords (banking and similar) in a password manager, and you probably should be, here's a low-tech way to create and keep track of very secure passwords for those special accounts.
Print an array of random characters on a credit card size piece of paper or card stock using a fixed-pitch font. Try to fill most of the card so you have plenty of characters. It should look something like this:
Print several copies and keep them in different places in case you lose one. Cary one in your wallet or purse. To make a password, draw an imaginary shape (square, triangle, letter "M", etc) through this array, defining a sequence of characters. All you have to remember then is the starting location and the shape, not the crazy random password that this produces. For passwords that you have to change on a regular basis, you can just shift the position of the shape to make a completely new password without having to make much mental adjustment to remember it.
If one of your cards ever falls into evil or unknown hands (wallet lost or stolen, for example), make new cards with a new array, and use one of the old ones one last time to access your accounts and change your passwords. It's unlikely that a wallet thief would know what it is for, but don't let that give you a false sense of security. The "draw a shape on a card" technique is really very weak encryption for any smart hacker who has possession of the card and either knows or deduces its purpose.