This is by no means comprehensive, but if you want to see some data, nick_charles did some analysis of some cables a while back. There were some differences, even in the audible frequency range! (just really really small ones that most probably nobody could hear, as would be expected)
http://www.head-fi.org/t/405217/my-cable-test-enterprise
Certainly in some setups and fringe cases, you could get problems from EMC, ground loops, etc., though generally not for a cable that goes to headphones and back. In almost all circumstances don't expect any real differences, certainly not to the effect that some people describe. The cable geometry and construction is more important than the materials too. As mentioned earlier, if you have a really long and thin cable (higher resistance) and a low impedance load, then the resistance of the wire is non-negligible and that could create an audible problem as well. Again, that generally won't happen for headphone cables, but that's a very valid concern for hooking up speakers.
Edited by mikeaj - 2/13/12 at 3:08pm
