Young's experiment can, in theory, be performed one photon at a time -- with identical results.
If either slit is covered, the individual photons hitting the screen, over time, create a pattern with a single peak -- much as if gunshot were being poorly aimed at a target.
But if boths slits are left open, the pattern of photons hitting the screen, over time, again becomes a series of light and dark fringes.
This result seems to both confirm and contradict the wave theory. On the one hand, the interference pattern confirms that light still behaves much like a wave, even though we send it one particle at a time.
On the other hand, each time a photon with a certain energy is emitted, the screen detects a photon with the same energy. Since the photons are emitted one at a time, the photons are not interfering with each other -- so exactly what is the nature of the "interference"?
Modern quantum theory resolves these questions by postulating probability waves which describe the likelihood of finding the particle at a given location -- these waves interfere with each other just like ordinary waves do.