How to rebut denials of the existence of photons? Recently I have encountered several engineers who do not “believe in” photons.  They believe experiments such as the photoelectric effect can be explained with classical EM fields + quantized energy levels in atoms. There is a 1995 paper by Lamb along these lines entitled “Anti-photon”.
What are some easily understood experiments that prove the existence of photons, which I can point to in discussions with anti-photon advocates? 
 A: I would tell them to re-read and understand that paper, and know that few spectroscopists would disagree with it.  The point is that far too many people use the word "photon" without knowing what a photon really is or under what context the word can be used.  For the vast majority of applications a semi-classial conception of the radiation field is adequate. The author wants to discontinue the use of the word, not negate the real existence of that entity, as defined through a rigorous QED treatment of the radiation field.
A: Photon counting statistics cannot always be explained by classical fields. In these experiments, the state of the field is monitored continuously by a photodetector. I believe these represent one of the clearest experimental demonstrations of the quantum nature of the radiation field. 
For example, in observing the emission of photons from a single atom, one never detects a second emitted photon immediately after the first. This is due to the fact that after a spontaneous emission event the radiation field is in a Fock state with a well-defined number of photons. This "anti-bunching" effect was observed by Kimble et al. in 1977 and is reported here. It is not possible to explain the experimental intensity distribution as arising from an underlying classical electric field, even if we allow the field to fluctuate stochastically. The quantum theory of light was thus found to be necessary. 
Note that these conclusions do not depend on the use of photomultiplier tubes in the detectors or anything else to do with the photoelectric effect. One needs only some device that is capable of measuring the intensity of light with sufficient time resolution.
A: The issue here, I believe, is not existence of photons, but the fact that people may choose terminology and concepts they find appealing.
The word photon has been coined long ago for an idea that is quite far from the current views on light and the meaning of the word has been evolving many decades.
Its current use in textbooks and papers is quite broad and may be regarded as inconsistent - in one situation photon is a dot on the detector screen, in another it is something that spreads the whole experimental setup, in yet another it is quantum of energy that gets absorbed in a tiny region of space comparable to an atom.
Such liberal use of a word may not appeal to people who like their terms general  and clear, which is why they might prefer the term EM field (even in quantum theory) instead.
The possibilities of mathematical modelling of light by continuous fields have  evolved to the point where they can account for many experiments that were previously thought to require the idea of particles of light. Photoelectric effect, double slit experiment, black body radiation may be approached from the mathematical standpoint where light is described by continuous fields.
In the end, explanation of an experiment involving light with words and mathematics is just that, and proves nothing about what the light "really consists of".
A: Photons are observed as radiation with a given spin and other properties. As such, they do exist.
But according to the principles of time dilation and length contraction, from their (hypothetical) proper point of view, they would be reduced to a single momentum. Their proper time would be zero, the distance of their geodesic (and also the spacetime interval) would be reduced to zero. That means that from their (hypothetical) point of view, nothing would be moving - just a momentum transmitted directly without a wave from one electron to another, no particle.
Of course, this is a hypothetical, calculated reality because photons are not observers, and they have no reference frame. But according to the principles of time dilation and length contraction, we can also be sure that our observation does not correspond to reality.
