In a two slit interference experiment, if you measure through which slit the particles move, you'll destroy the interference pattern. You can also do this in the classical regime, but usually this has a trivial classical interpretation. E.g. you could give the polarization of photons depend on which slit they move through. Then the polarization state of the photon carries the "which path information" with it. You then don't get an interference pattern. In the classical interpretation, you can simply say that the electromagnetic field components of the light coming from the two slits are orthogonal w.r.t. each other. Instead of giving the photons a polarization one could, in principle, collect the "which path information" without affecting the state of the photons. If you could do this fast enough, you could have classical electromagnetic waves which according to classical physics should interfere, but they will fail to do so.