Password managers have been around for years, some store individual passwords for individual sites, some integrate with your browsing and apply stored passwords when required, others provide a portal allowing you to choose the site you wish to navigate to and let the password portal log you in. I on the other hand have absolutely no idea of what my list of passwords look like, equally so I don't store them online, have a note of them; I simply don't know what they are.
For a number of years I have been using a tool called PasswordMaker, this tool is available for all the main browsers (in fact the relatively recent addition of the Chrome extension paved the way for me changing my main browser choice). There is also an online version should you be unable to install extensions in your browser, and to round off the coverage mobile versions for both iOS and Android.
The tools' premise is a simple one; based on the current URL and a single Master Password the tool will calculate and generate a secure password or 'Digest'. The process used is a one-way hash algorithm meaning it would infeasible to invert the output and importantly should an unscrupulous person get hold of one of your generated passwords, it would be infeasible for them to use that to work out your other passwords. Additionally there are various modifiers that can be set meaning that even if you were ever to expose your master password, it still wouldn't necessarily assist in finding your site passwords. In short, it's very secure.
You can delve into the inner workings of the encryption process here.
The upshot is I am left with remembering a single master password. I have the option to store that in memory for the browser session, encrypted on disk or not at all.
So you can now sit back and relax knowing you've got strong, secure passwords for all your sites and you don't even need to remember them...just don't forget the Master!