Password security involves a broad set of practices, and not all of them are appropriate or possible for everyone. Therefore, the best strategy is to develop a threat model by thinking through your most significant risks—who and what you are protecting against—then model your security approach on the activities that are most effective against those specific threats. The Electronic Frontier Foundation (EFF) has a great series on threat modeling that I encourage everyone to read.
In my threat model, I am very concerned about the security of my passwords against (among other things) dictionary attacks, in which an attacker uses a list of likely or known passwords to try to break into a system. One way to stop dictionary attacks is to have your service provider rate-limit or deny login attempts after a certain number of failures. Another way is not to use passwords in the "known passwords" dataset.
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