Since it’s impossible in current theories, speculation about exceeding the speed of light in a vacuum is bound to be hollow.
However, when light passes through a medium like water it gets slowed down. It can then be the case that things can be moving faster than the speed of light in that medium. (But still slower than 3 x 10[sup]8[/sup] m/s, the speed of light in a vacuum.) What happens then is actually fairly analogous to what happens with sound: the object overtakes any light it emits and so the light builds up into a “shock wave”.
Such Cherenkov radiation is a pretty common phenomenon where subatomic particles are concerned. For technical reasons, it usually appears blue and this is, in fact, the source of the blue glow you see when radioactive material is contained under water (and so in the old Hollywood stereotype of a nuclear reactor). The particle radiation is sufficiently fast that it’s emitting Cherenkov light as it passes through the water.
Since the shape of the “shock wave” sensitively depends on how fast the particle that emits it is going, the effect is used in various high energy physics experiments where you want to measure particle speeds. You have a tank of water and light detectors round the side to detect the shape of the flash; this is the best known example (though the design is prone to rather odd accidents).
As for sound, I’m fairly sure the sonic boom was first predicted on purely theoretical grounds by Mach, but I can’t find a specific reference.