Latin: sinister and dexter, I think they are used for parts of organs (eg liver); one source notes occulus sinister being used in the abbreviation OS for left eye.

Greek dexios and aristeros ... well dexter come from dexios", as does the chemical suffix -dextrin. Aristeros* is a euphemism, it means something like "best" (I wonder if that's the origin of 'put your best foot forward') ... I'm told that left-sided things were unlucky to the Greek speaking peoples and Greek language apparently compensated by describing that position positively.

The "left-side are unlucky" thing affects the Latin example as well as the Greek, at the very least in the way that English derived words get used: compare "dexterous" (modern English connotations of "able, agile") versus "sinister" (modern English connotations of "evil, subversive").

It's an interestingly deep rabbit hole in language etymology just how much "left" gets besmirched and "right" gets positive connotations. (The fact that "right" is also a synonym in English for "correct" being another bit of evidence.)