We are used to the quantum weirdness of the two-slit experiment, but things get much weirder than that. In the 1980s John Wheeler proposed a "delayed choice" gedanken experiment. This would make a two-way interference experiment (allowing either two paths or just one) a little more interesting by delaying the choice of whether or not to allow two paths until after a photon would have had to commit classically to one thing or the other.
Now, for the first time, Vincent Jacques and colleagues from the École Normale Supérieure de Cachan, East China Normal University and the Laboratoire Charles Fabry de l'Institut d'Optique have made an almost ideal practical realization of Wheeler's gedanken experiment. Their experiment uses a quantum random number generator to decide whether to allow one path or two, and makes a space-like separation between the photon entering the interferometer and the decision being taken. The results show that quantum mechanics triumphs over common sense yet again.
Further reading
Vincent Jacques et al. 2007 Science 315 966.