I personally have (and preach) a password system using a "root" password shared amongst many passwords, plus a unique password component.
So for Gmail my password might be
F00@$DF and for another application it would be
3p1cp@$$w0rd. The idea is you get a large amount of entropy out of the root password while easily remembering it (because it's always the same), but since it's not all of the password, if someone has one of your passwords, they still don't have them all. The unique part of the password is easier to remember because it can be shorter while still a very large character count and large amounts of special characters.
Is there a term for this sort of root + unique password scheme? I'm trying to look for good articles about it or any potential pitfalls of it but I have no idea how to refer to it. It's also very hard to explain at first.