Most know Occam's Razor - unnecessarily complicated explanations are less likely to be correct.
And most know Hitchens' Razor even if not by that name: "What can be asserted without evidence can be dismissed without evidence." Of course, dismissed doesn't mean ruled out, just disregarded despite not being rebutted.
Sagan's pronouncement that, "Extraordinary claims require extraordinary evidence," can be called Sagan's Razor.
Popper's assertion of falsifiability can be called Popper's Razor: "For a theory to be considered scientific, it must be possible to disprove or refute it." The implication is that ideas not considered scientific can be disregarded, but they also cannot be ruled out, either. They go to the bottom of the list, like claims involving supernaturalism, but not off of it.
There are a few colloquialisms that do the same kind of thing. "Never attribute to malice that which can be adequately explained by incompetence or stupidity" has been called Hanlon's Razor.
"If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck" can be considered a Razor (the Duck Razor?).
And we had one in medicine for evaluating symptoms - "When you hear hoofbeats, look for horses, not zebras," zebras being rare diagnoses. Rare things occur rarely, so rule out likelier (and also more time-sensitive) diagnoses first.
Anecdote: There used to be a site called Pete's Pond set in a game reserve in Botswana that was a real-time camera (now defunct) of wildlife drinking at a pond. One night, I was watching and heard clop clop clop, and thought to myself, that's odd - horses in Botswana. Then I saw them when they came into the light. Zebras. Of course. I was embarrassed at myself and had a good laugh recalling the medical razor. I wonder if African medical students are taught that when they hear hoofbeats to think zebras, not horses. Context is everything.