1. I don't care if somebody gains access to my account
2. I do care if somebody gains access to my account
I use the same password for all the websites on the first category. It should be at least 8 characters long, consists of a made up word with some numbers and characters. Example: 7%Frifells. I drop the special character on websites that don't allow them in passwords and then it's a matter of failing to log in once and trying without it.
I use a different "xkcd" password (https://www.xkcd.com/936) for every website on the second one. Those are essentially catchphrases which I end up associating with the website I use them for. They consist of several words with numbers and special characters (using the example in xkcd, mine would be correctHorse?1batterystaple!).
So, I have to memorise about 8 passwords, all which make sense to me. In addition I have a password reminder file which consists of the website URL and the first two/three characters of the password. I don't bother adding completely unimportant websites from the first category.
If my password from category 1 gets compromised then it's a bit of a hassle to change the password on all the websites on the files, but no harm done. If a password from category 2 gets compromised then it doesn't affect the other websites.
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I wish a lot of websites would realise they can be password-less. Pinterest is a good example. I have never posted anything, they don't have any personal or financial information from me and if and the only reason I registered was because I wanted to search something there once, and they made me register for that. Same goes to Quora and many other websites. I think all those should allow registering without a password but limit the functionality of those accounts.
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Edit: formatting