I'm actually surprised that the 4th Amendment isn't referenced more frequently in refutation to the asinine "nothing to hide" position.
"Nothing to hide" is thematically similar to the groan-inducing "Do you want the terrorists to win?" arguments against civil liberties, in favor of increased security measures, proferred and popularly supported in the mid-2000s. (Sadly, many of the legacies and artifacts of that position still persist).
The answer to any of these half-baked arguments should always begin with something along the lines of "Because we're better than that." Because we have a constitution that assumes we're good people, and that protects our civil liberties from invasion. Because these things are so fundamental to our nation's purpose that giving them up is much worse than being attacked. Giving them up threatens the very purpose of the country's founding.
Even to entertain these arguments, i.e., by trying to cite examples of areas of privacy or liberty that are negotiable, areas that aren't, and so forth, is to stoop low. It is to lose before the argument has actually begun. It is to accept the faulty premise that privacy is about hiding something -- that it is an active attempt to conceal information from the world. No, privacy isn't the action being taken. Invasion of privacy is the action. Privacy is simply a state of being, and one to which we have an inalienable right.
Privacy isn't something we opt into; it is something we don't even really consider until we are made, or compelled, or asked to opt out. "Nothing to hide" begs the question. It assumes, as a foregone premise, that privacy is an opt-in decision that we consciously undertake in defense of something (and that something is implied to be onerous or illegal). This is just fallacious logic, plain and simple.
It's unfortunate that a right to privacy wasn't inumerated directly in the constitution, but was instead defined indirectly. This is one of those areas where the founders really couldn't have known how far technology would go, and how important something like privacy -- which may have been taken for granted back then -- would become 200+ years later.