Everyone should be using a different password for every website. Period.

But it's so hard to remember all those passwords.

Then don't. Use a Password Card:

https://www.passwordcard.org/en

A password card is a randomly generated, card of characters that can be used for passwords.
It looks like this:





The password card is something that you can print out and keep next to your computer, or on your person so you can use it to keep track of all the passwords for all of your web sites.

Use it like a crossword puzzle. Just pick a character to start and continue for 8 or more characters. All you have to remember is what row or column you started with and the card takes care of the rest.
For example, I can start with the character and go from top to bottom for my online bank password. The password it created, "v9PQHCvm" is strong, 8 characters and includes uppercase, lowercase and numbers.
Next I can use the Heart symbol and start with the cyan colored row (row 8 ) and go across until I each 8 characters... or 10, or more. As long as I remember heart/cyan, I will always have the password.
As you can see the possible combinations of passwords on one card are huge.

When you load up the password card web site, it generates one for you. Click the Reset button if you want a new card randomly generated. There is also an option to include special characters to make your passwords even stronger.

Now there is no longer an excuse. Separate passwords for every website!