The basic idea in special relativity that nothing can travel faster than the speed of light is a consequence of the Lorentz transformation equations, which if they hold exactly, it would indeed be true that getting to the speed of light would require infinite energy. There are, however, indications that Lorentz invariance indeed does only hold as an approximation. There is a growing body of evidence, both theoretical and experimental that shows that some of the predictions of Lorentz invariance do not exactly hold.
First from a philosophical standpoint. The two pillars of modern physics of the present day, quantum field theory and general relativity, both developed and use equations that describe the vacuum that look remarkably like the equations of fluid mechanics, i.e. they describe free space as though it were a material medium. In classical fluid mechanics with the linear partial differential equations that are used to approximate the behavior of the fluid, we have the result that exceeding the wave speed of the underlying medium would result in infinite pressure. Naively, we might then say that it's impossible to break the speed of sound in a medium. Of course, everyone knew that these linear equations were only approximations and more complicated nonlinear equations needed to be developed to describe the behavior of the fluid at transonic and supersonic conditions. From this point of view, we might say that the same situation might be true for these equations that are being developed at the frontiers of modern physics.
A seeming sign that Lorentz invariance does not hold exactly comes with the formulation of quantum electrodynamics, and Richard P. Feynman's infamous renormalizations. The requirement for mass and charge renormalizations in QED is a signal that Lorentz invariance is not quite holding up. These deviations in intrinsic mass (not to be confused with the relativistic mass increase) and charge occur not only in the presence of very strong electromagnetic fields such as near an atomic nucleus, but also as the speed of the particle increases, meaning that the deviation from Lorentz invariance actually gets worse with increasing speed. Which is exactly what one would expect with the analogy to a material medium given above. One might wonder that perhaps Feynman's cavalier attitude to the mathematics in that instance has obscured something more fundamental. The fact that subsequent quantum field theories have followed the same pattern may have made this obscurity even worse.
General relativity also gives indications that Lorentz invariance should only be taken as an approximation. It is stated by the theory that in real curved space with real bodies inducing their own spacetime curvature, Minkowski space cannot exactly hold, in other words, Lorentz invariance does not exactly hold in real curved space. General relativity also seems to give a similar result as quantum field theory in that that deviations from Lorentz invariance get worse with increasing speed.
So what does this all mean? If Lorentz invariance can be shown to not exactly hold, then it is indeed likely that all of its other predictions are approximations as well, that in particular its prediction that physical objects cannot move faster than the speed of light is an approximation, and that at high enough energies, it is possible to go faster than c. I know, I know, this is all highly speculative, but then again, it seems that this doctrine of Lorentz invariance has reached the status of dogma among scientists, and anyone who questions its "absolute truth" is immediately labeled as a crackpot propagating heresy and any possibly valid arguments that might have been made are discarded solely on that basis. This is not the way science progresses.
The original source for much of this wu (which I have paraphrased and summarized) comes from the discussion in http://science.slashdot.org/article.pl?sid=01/02/09/1312244&mode=thread&tid=134, "Experiments Poke Holes in Quantum Physics". See especially postings written by rgclark. The original Slashdot article had to do with the anomalous measurements of the muon magnetic moment that cannot be derived from modern theory, and could be further evidence that the Standard Model is invalid, and that the Lorentz invariance it takes for granted cannot be perfectly accurate.
And by the way, going faster than the speed of light does not necessarily imply a violation of causality: it could be that there is a special inertial frame of reference and that the principle of relativity needs to be abandoned, yet another idea considered heretical by most physicists.
Update: Some Australian researchers from the University of New South Wales have today (August 7, 2002) announced that they have detected some deviations in the value of the fine structure constant while observing light from a distant quasar 12 billion light years away, meaning that the light was generated only a short time after the creation of the universe. The value of α that they obtained was slightly higher than the traditionally measured one. Since the fine structure constant depends both on the electronic charge and on the speed of light, it could mean that either the value of the elementary charge has increased since the birth of the universe, or the speed of light was slower. Other observations they made rule out the possibility that elementary charge has changed as it would violate the Second Law of Thermodynamics. This could be construed as further possible evidence that Lorentz invariance is inexact. It seems the fine structure constant node already has some wu's about related discoveries. The article is: http://theage.com.au/articles/2002/08/07/1028157961167.html