Particles in particle accelerators are given immense amounts of energy, and none so far have surpassed the speed of light. According to Wikipedia (and the math seems to check out), protons in the LHC are traveling at about 99.999999% of the speed of light. Remember that the point of the accelerator is to get the particles to go as fast as possible; every new design for the past 80 years or so has only manged to add more 9's to that number. And if a particle had gone over the speed of light, we would surely know, if only because of the incredible precision with which these experiments are done. Just to drive the point home, a few years ago the OPERA team, due to some experimental error, though they had detected neutrinos moving faster than the speed of light by a factor of 1 in 40000.
No amount evidence is equal to proof, but this is surely as close as it gets.