A couple of interesting things in this thread.
1.) The article Jude posted is an abstract for a meeting that seems to be geared more towards industrial applications. It's certainly not written well and contains fairly significant errors. The idea that atoms in the lattice of a metal "get in the way of" electron movement is ridiculous.... atoms are almost completely space, and electrons don't "fly" through space like a BB anyway. I'm not necessarily disputing their findings, but they aren't of the electrical kind. If I'm reading the abstract right, their findings are based on the physical observation of the crystal lattice tightening up and being purer post cryo treatment, which is not really disputable, and that the copper exhibited better welding properties post cryo treatment. The idea of the copper being a better thermal and electrical conductor post cryo treatment is presented, but nothing in the extract gives any clue as to what empirical methods were used to determine this, other than SEM, which obviously doesn't measure or have anything to do with electrical conductivity.
2.) It's not a matter of the impedance of a wire that affects it's "sound". The impedance of a metal conductor is very low relative to that of a speaker, etc. What matters is that the impedance has to change with frequency to a significant enough degree that it affects the frequency response of the system above the baseline of that system. I don't think there has been any study that showed wire of one kind or another does this to any significant (i.e.- humanly observable) degree. Not that a study showing this isn't out there, I just haven't seen it.
3.) I read a very interesting article from Nelson Pass that hinted at the effects of cables on sound being due to two probable scenarios... how they load the amplifier and the corrosion of the contact points. For long cables, amplifier loading is important and cables of different impedance can cause the amplifier to behave different, even leading to HF oscillations, etc. So it's not the cable itself that "sounds" different, but the amplifier behaving differently for different cables that causes the sound signature to change. As headphones tend to have short cables, this isn't usually an issue for headphone enthusiast. The second idea, and one that makes a lot of sense to me, is the idea of degradation of the contact points (the solder joints and the plugs/jacks themselves). He made the point that often when people compare cables, they compare a new cable to an older cable that they have had for a while, where corrosion (even corrosion that is nearly invisible) at the contact points can have a dramatic effect on the sound signature. I have a feeling that much of the difference heard in cables is due to this phenomenon.
4.) As far as cables sound goes, I think people worry too much about the materials used and less about the method of construction - i.e.- braiding technique, insulation material, etc. My guess is if there is any difference from one cable to the next, the latter is more likely a cause of this difference than the former.
5.) All of this being said, I do think there is still good reason to use a more expensive wire besides sound: construction quality, flexibility, and visual impact are all legitamite reasons for me. No one needs expensive china; it certainly doesn't make food taste better, but the quality of the meal is no doubt enhanced for many people. The same goes for nice looking gear. It might not make the sound better, but for many (including myself) it makes the quality of the experience better, not to mention the comfort if the wire is more flexible (nothing worse than a stiff headphone cable, imo).
As a side note, for all of the analysis I gave above, I noticed something really bizarre in a bad cable that I had a few weeks ago and I'd love to hear an explanation from someone if they can think of one. One of the cables I had made a while back had a solder joint on the ground wires come loose. Obviously the connection was intermittent. What I found completely amazing was that in some of the music played through the bad cable there was unmistakable weirdness in the distortion caused by the bad joint. Of course the music was quieter throughout, but in several songs the bass, bass drums, and the high hat as well as some of the guitar came through, but the vocals were completely gone, in other there were background vocals (harmony) but none of the lead vocals. Other songs showed the same weirdness as far as specific sections of the song making it through the cable, and other sections not (and no, it was definitely not a stereo issue; lead vocals tend to be balanced L/R, plus it was a common ground joint that was bad, not the L or R joints). This shook me a little bit, as I've tended to not believe that a cable could make a difference in the details of say the female voice vs. another cable, as you often read in reviews. However, I found this to be a clear example of an electrical joint (bad though it was) not only causing distortion, but causing distortion at different levels for different sections of the song. Any comments?