What are the connotations of the word "Greetings" when used as a greeting? I am British, and I have rarely heard "Greetings!" used as a greeting in the UK. I associate it in my mind with Commander Data in Star Trek: The Next Generation, because I seem to remember he used it a lot. So to me it connotes geeky, formal and stilted. However, I appreciate this may not be accurate.
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I doubt there was ever a time when "Greetings!" was a common salutation. Because it's perfectly comprehensible, some people might assume it's a "dated" usage - and by association, perhaps they might therefore assume it's formal/stilted, but I don't think that's really accurate.
In "real-world" contexts today, it's usually (but not always) used facetiously. But because it's a relatively uncommon non-idiomatic form, it's often used in contexts where the intention is to convey that the speaker is somehow "exotic" and far removed from everyday life as we know it.
Consequently, it's often used in science fiction/fantasy novels, movies, etc., which is why OP also perceives geeky associations. It might also turn up in "historical fiction" - but again, I think that would be because the writer wants those exotic/distant connotations, rather than because they've researched the matter and are accurately reflecting the usage of a bygone age.
So if a native English speaker greets you with "Greetings!", you can usually assume he's being flippant/jocular. With a non-native speaker, you could perhaps infer he's not fully fluent.
Several dictionaries don't agree with the notion that it is somehow facetious or jocular. It may be, but I would definitely say that it is normally used as a formal means of acknowledging someone.
The Cambridge dictionary, for example, has this to say...