Before very recent times, the word "worship" meant merely and simply and only "to honor." The word worship is exactly equivalent to the modern English "honor [outwardly]" because "honor" comes from the Latin honor, whereas "worth" is the Old English equivalent meaning the same thing.
The Old English word weorþscipe (worthship) is related to the word "worshipful" in the same way that "to honor [someone]" is related to "honorable [person x]." -bilis (able/ible) comes from Latin, and -ship or -shipful from Old English. But the meaning is the same. Just as "ghost" comes from "geist" from its Germanic root, but "spiritus" is the origin of "spirit." Both refer to the same thing. Everyone has heard of the "spirit of the times" (the time-ghost, the zeitgeist). Two words, meaning the same thing, from two different languages. Well, the same is true of "honorable" (think of modern courtrooms) and "worshipful" (meaning the same thing) in archaic yet still used religious rites. "Adorable" originally meant "worthy of worship [adoration]" and so on. Different etymologies but the same meaning.
Naturally, then, honor can be given to God, but also men (such as kings), both by outward signs - even the same ones, since the difference between honoring God is in the heart, not in the kind of action, unless the action is in and of itself something which only God is worthy of.
Going into Greek and Hebrew doesn't change anything, since the usage is the same as in English. The English word comes from "weorþscipe" (worthship) which means to show someone honor (which is where we get the word worth, something worth or worthy or honor-able enough to fight for). From this, a derived term "worshipful" is used in some religious contexts in a similar way to how certain courtrooms call people "honorable" (which is what worshipful meant).
But one example is:
1 Chronicles 29:20 And David commanded all the assembly: Bless ye the Lord our God. And all the assembly blessed the Lord the God of their fathers: and they bowed themselves and worshipped God and the king.
In other words, one only knows from the context whether the honor given to a man or God is given as to God or as to man, by its condemnation or approval, not by the act itself of 'worshipping.'
It's in the simple sense that the Magi presumably 'honored' or bowed to "He that is born king," not because they somehow knew the mystery of the God-man, but because He was royalty, and one 'worships' - honors - royalty by such outward signs of respect.
Where this does change in Hebrew and Greek and Latin, at least in Biblical usage, is when a different underlying word translated worship (there are several, all of which fall under "honor") specifically refers to te worship of a divine being in a liturgical, sacrificial way. This is usually the case when one sees the word "serve," actually, rather than the word "worship." Here, it's the word for "worship" or "honor."