Occasionally, people still express questions in this form:
"What say you to a nice cabernet?"
"What think you of our impetuous young friend?"
These aren't standard constructions, however, and their very stiltedness imparts a note of amusement or irony to the question. No such sense attaches to, for example, "How dare you speak to me like that?" or "Need I say more?"
But the first two examples I gave also have this difference from the second two: They don't appear in tandem with a following verb. The expressions "dare...speak" and "need...say" are thus operating in a different way from "say to [this]" or "think of [that]."
A genuinely archaic example of such a construction (from Ezekiel 34:18 in the 1611 King James Bible) involves "seemeth":
"Seemeth it a small thing vnto you, to haue eaten vp the good pasture, but ye must tread downe with your feet the residue of your pastures? and to haue drunke of the deepe waters, but yee must fonle the residue with your feete?"