As per in the title. If it turns out that neutrinos do travel faster than the speed of light, how will the success of special relativity be explained? My apologies if this has been asked before; I've just browsed through few questions, and I couldn't find one that matches (although it was slightly touched on in one answer).
The various theoretical options are very different in nature, and the answer to this question almost defines the option.
1) Relativity is wrong, there is objective absolute time, Lorentz symmetry is emergent (as in electrodynamics before Einstein), and going faster than light doesn't create any time-loop paradoxes.
2) Relativity is valid, but neutrinos, not photons, travel at the actual relativistic speed-limit; photons have a small mass, or photons are confined to a braneworld while neutrinos can take shortcuts through hyperspace.
3) Relativity is valid, neutrinos are tachyons (or the OPERA result manifests some other sort of spacelike correlation), and something (Deutsch's multiverse, Hawking's CTC instability, weakness and/or uncontrollability of the effect, QM itself actually comes from CTCs...) prevents it from creating a time-loop paradox.
It should be extremely difficult to turn any of these 3 options into a fully working theory capable of reproducing the standard model. The odds are still heavily against OPERA having actually observed FTL neutrinos.
Let me rephrase your question:
If it turns out that light is really particulate how will the successes of Maxwell's equations be explained?
If you are a physicist you know the answer to this: by a quantum mechanical framework that incorporates Maxwell's equations.
The history of physics shows that whenever a data discrepancy to a widely accepted theoretical framework appears, the resolution of the paradoxes is in an expansion of the framework. The old data are consistent with the putative new theoretical framework by logical necessity: that is how the new framework is attained, by reconciling all data, conventional and new.
This paper by Feinberg has some interesting points about Tachyons stating that they might be compatible with Special Relativity and Quantum Field Theory. The essential points there are that Tachyons would have to be Spin-0 electrically neutral particles which despite the integer spin would obey a Fermi-Dirac statistic. I don't know if Spin 0 can somehow validly be attributed to Neutrinos, but another nice idea I read about (but sorry I forgot the source) was that the Neutrinos themselves are Tardions but some immediate Tachyons caused the FTL signal.
The basic explanation Feinberg's paper gives is that in QFT one cannot truly distinguish creation and annihilation events and therefore any apparent time-paradox would "simply" be a mixed up interpretation of these events.