What do we mean when we say it today?
Ever since Nicole Kidman and Ewan McGregor belted out "Come What May" in Moulin Rouge, this phrase has made one heck of a comeback. These days, this phrase has a couple of meanings. It can be said as a way of absolving blame or guilt, as in, "Whatever comes to pass will pass. We have no control over it. It's out of my hands." You get the idea. But it can also be an expression of faithfulness and loyalty, as in "I'll stick by you, no matter what comes down the pike." And, of course, there's the whole "Que sera sera, whatever will be will be" thing. A sort of, "Meh, we'll see what happens, and in the meantime we won't sweat it" type of attitude.
Shakespeare came up with "come what may," but he certainly wasn't the one to come up with the idea. Even in Medieval times, the French said something to the effect of "let it avail what it may," and the Spanish had their own version: "whatever will be, will be."
No matter what language you speak, the meaning is the same. Come what may.