You guys got me curious, so I tried it this afternoon with upside down ceramic coffee cups (Thanks Audiobugged). I'm actually a little surprised at how easy it is to hear the effect. Transients, like acoustic guitar plucks, are more dynamic. The overall tonality is very slightly brighter. One not entirely positive effect is the soundstage got shallower. I suspect if I toed out my speakers a little bit more I could make the soundstage as deep as it was before. I found I could vary the soundstage depth slightly by only lifting part of the speaker cable off the carpet.
In my system, the effect of lifting the cable off the floor is no where near as strong as changing ICs, for example, but it is audible.
If I had to guess as to the technical reason for this, it is the poor quality of the dielectric of the carpet that causes the degradation of sound. In particular, its dielectric absorption characteristic. It has been known for many years that capacitors with low DA are required for high fidelity audio, e.g. polystyrene, polypropylene, and teflon. Teflon is also widely used in cables. I think Rushton got it right - the signal, as it passes through the speaker cable, charges the dielectric, then the dielectric discharges somewhat lagging the electrical signal which muddies the sound. Air is the best dielectric possible, so this is why the cables sound better in the air than lying on the carpet.