Basically, I can't stop wondering why light (the photon) is so special, compared to all the other particles known (and unknown) to modern day physics.
Could it be that there exists an upper limit on speed that is instead a property of another "entity" (particle / wave), other than the photon?
A question obviously inspired by the recent very slightly possible superluminal neutrino findings
Answer
The reason is partly historical accident, and partly experimental support, but in the end a certain salient property of light itself.
James Clerk Maxwell inferred, from his laws of electromagnetism, that there exist electromagnetic waves. Computing the speed at which they travel, he found that this speed was in close agreement with the observed speed of light. And so he conjectured that light was an electromagnetic wave. However, his equations make no reference to a medium (beyond bare electric and magnetic fields) in which the electromagnetic waves were to travel. The waves travelled at the fixed speed c in vaccuum — but relative to what, or to whom? There was no answer.
The "luminiferous ether" was conjectured to solve this problem. It was defined simply to be the medium in which EM waves (and light) travelled; and if you moved relative to the ether, then you would notice differences in how light travels relative to you. Michelson and Morely tried to establish how quickly the Earth moved relative to the ether, at different times of year (to account for how the Earth revolved around the Sun) with precision equipment, but could find no detectable difference at all in the speed of light in different directions, at any time of year.
FitzGerald and Lorentz tried to explain this negative result by means of a length contraction of any objects not at rest. There wasn't a good justification for why this should occur, but it did explain the results. And people tried in various ways to figure out what was going on, with ambiguous success.
Once Einstein simply decided to accept as an (experimentally supported!) axiom that the speed of a beam of light in vaccum is the same for all observers, and worked out the consequences, the length contraction postulated by FitzGerald and Lorentz fell out as an immediate corollary. Another corollary was that it would require an unbounded amount of energy to accelerate an object to speeds approaching that of light, from rest in any reference frame other than that of a beam of light. And so unless you think you have access to a very-literally infinite source of energy (and in finite time at that), you cannot accelerate anything up to the speed of light.
In all of this, what made light special was it's property of travelling at the same speed for all observers: predicted by Maxwell, and supported experimentally as well as one can without the use of high-velocity spacecraft, not to mention indirectly by all of the empirical support (including the precession of the perihelion of Mercury's orbit, starlight deflected by the Sun, and the successful operation of GPS as it is designed) for Special and General Relativity themselves.
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