This is prompted by the strong claims made in Science 332, 1170 (2011) to have observed trajectories of photons, "something all of our textbooks and professors had always told us was impossible". I'm suspicious of this claim because they work entirely within quantum theory, and it seems to me that in making weak measurements at two points on what they say is a trajectory, they do nothing else than make unsharp measurements of incompatible observables, a concept that was first introduced, to my knowledge, by Busch and Lahti in Phys. Rev. D 29, 1634–1646 (1984), and that is now much used in quantum information. Certainly observables that are at time-like separation are in general incompatible, so an unsharp measurement approach would seem applicable.
A brief account of the Science paper mentioned above can be found here, amongst other places, and a few quotes can be found here, but, this being Science, I couldn't find a preprint. I was first alerted to this paper by a page at the BBC. The claim highlighted by ZapperZ, "Single-particle trajectories measured in this fashion reproduce those predicted by the Bohm–de Broglie interpretation of quantum mechanics (8), although the reconstruction is in no way dependent on a choice of interpretation", seems to me particularly egregious, insofar as both their choice of what experiment to do and of what to do with their raw data seem partly driven by the form they want to present their results in. It seems entirely possible to present the data in terms of unsharp measurements and POVMs, which would give relatively less support to the de Broglie-Bohm interpretation.