The results that came out of CERN showing that neutrinos reached a detector a nanosecond or two faster than a photon would are fascinating. I suspect it will eventually turn out to be a systemic error in the experiment, but if not, wow.
I'm comforted in knowing that both special and general relativity have held up extremely well in experimental results. I'm not sufficiently versed in the details of the theories to know how exactly faster-than-light travel would affect its workings, but I do know enough to know that it would blast a sizable hole through it. What an opportunity that would be for us to learn more about the universe!
Of larger import, however: if one of our most "incontrovertible" facts about the universe is proven wrong, what else do we think we know, that maybe we don't?