Does the speed of light in vacuum define the universal speed limit? 
*

*Is light the thing causing the universal speed limit to be $299\,792\,458\,\mathrm{m/s}$? So the universal speed limit would be different if light travelled faster or slower?

*Or, is $299\,792\,458\,\mathrm{m/s}$ the universal speed limit anyway and light just goes that fast? Light is just something we commonly associate with it because it goes super fast.
 A: Even if nothing propagated at the speed $c$, it would still be a universal speed limit, and we could still measure it.
In fact, it's not impossible that light has a (very tiny) mass in reality. If it does, that wouldn't change anything about special relativity. It would make teaching it even more of a nightmare than it already is, because we'd have to deal with a century of textbooks and popularizations that made the mistake of calling $c$ "the speed of light", but other than that it wouldn't change anything.
A: Above all, speed of light is the speed of propagation of fields through space. While light may be slowed down when crossing matter, fields (electromagnetic fields, gravity) are always propagated at c. One of the consequences is the "speed limit for causality" mentioned by DavidZ and the speed limit for transmission of information.
A: It's the second one: the reason the speed $299792458\ \mathrm{m/s} = c$ is special is because it's the universal speed limit. Light always travels at the speed $c$, whatever that limit may be.
The reason there is a "universal speed limit" at all has to do with the structure of spacetime. Even in a universe without light, that speed limit would still be there. Or to be more precise: if you took the theoretical description of our universe, and remove light in the most straightforward possible way, it wouldn't affect $c$.
There are many other things that depend on the speed $c$. A particularly important one is that it's the "speed of causality": one event happening at a particular time and place can't affect another event unless there's a way to get from the first event to the second without exceeding that speed. (This is sort of another way of saying it has to do with the structure of spacetime.)
A: The numerical value of $c$ does not have any fundamental significance. Rather it is the number we get based on the experimental fact (according to the number & unit system employed) . If some alien civilization ended with some different value of $c$ compared to us. Even that is not a problem. They will reach the conclusion that this is upper bound of the speed limit for any object, provided both civilizations governed by the same set of laws of physics. In that sense the speed of light is universal.
A: There is quite a bit of ambiguity in the question(s), so let me start by substituting electro-magnetic (EM) wave for "light."  Then, the "universal speed limit," is the speed at which EM waves propagate in "space." The reason I use space (not vacuum), is because it is the characteristics of space ($u_o, \epsilon_o$) that determine the speed of propagation of the EM waves.  If these characteristics were different, the value of EM wave propagation would be different (larger, smaller) but it would still be the universal speed limit.
As you can see, the correct option is #2, and since light happens to be an EM wave, it propagates at the universal speed limit.   
A: Articles published in Science and Nature say the speed of light is not constant:
http://science.sciencemag.org/content/347/6224/857 
 "Spatially structured photons that travel in free space slower than the speed of light" Science 20 Feb 2015: Vol. 347, Issue 6224, pp. 857-860
http://www.nature.com/nature/journal/v406/n6793/full/406277a0.html 
 Nature 406, 277-279 (20 July 2000): "...a light pulse propagating through the atomic vapour cell appears at the exit side so much earlier than if it had propagated the same distance in a vacuum that the peak of the pulse appears to leave the cell before entering it."
