A New Believer

I have listened to many systems over the years, and have never appreciated the difference speaker cables can make to a sound. In fact, I was so skeptical of the sound changes they can make that I have always not bothered with any special type of cables, generally going for generic (and dare I say it) roughly made ANY copper wire plugged in to amp and speaker. Well, imagine my surprise when I decided to do a blind test and listen to what difference cabling can make. Wow, my Vand 3A Sig's had been getting strangled! (some of you guys may want to strangle me if I told you what connects I had been using). So I am now a firm believer, cables DO make a difference.
Antipodes_audio, thank you for the comprehensive response.
Electrical engineers are very inclined to a reductive view of physics, dismissing many known issues as irrelevant at audio frequencies. By that they mean they are too small to be heard. Convenient when making a competent product, but how exactly do they know we can't hear them? As I say our ear/brain is incredibly sensitive to time issues, as that system is constantly separating out what we hear, its direction and its location, and that system is far more dependent on time-domain accuracy than timbral accuracy.
I am in agreement with this, up to a point. However, I would respectfully submit that there is a flip side to this line of reasoning. If we can’t clearly draw a line defining the boundaries of audibility, we also can’t predict when the point of overkill will be exceeded, and when the wrong parameters are being focused on.

It would seem safe to say that the chirp of a bird ten miles distant will be inaudible. Similarly, it would seem safe to say that one femtosecond of “time smear” will be inaudible, and will be swamped by other inaccuracies in the system as well. So there would seem to be finite limits to the extent to which reason, common sense, and technically informed “a priori” judgment should be deemed inapplicable to audio.

That applies to the cable designer, as well as to the consumer. How does the designer determine what design approaches to investigate, develop, and try out, when the point demarcating overkill for any given parameter is so nebulous? How does he know that he is focusing on the right parameters in the first place? How does he know that applying comparable focus and investment of time and resources to development of less expensive approaches won’t yield results that are just as good or possibly even better? Reasoned, technically informed judgment, common sense, technical knowledge, and experience all have their place.

And along the lines of a comment you made in your initial post above, it would seem safe to assume that those qualities, and just as importantly the motivations, of different designers will differ.

I cant believe that this is still talked about or debated. Anyone with any hearing left can hear the difference in all cables, if they just relax, and listen, its that easy. So many of the responses are about what you have read , or how you can measure such things, instead of just listening. They indeed make a difference, and if you cant hear it, you should get out of the hobby.
To Chrissain:

'They indeed make a difference, and if you cant hear it, you should get out of the hobby.'

Is your decision final, or do I have a right to appeal?

I tend to agree. We don't know, and we can't know - we can only cautiously make assumptions. I reckon that is why we have to rely to some degree on what we think we hear when we listen to something, rather than expect a scientific explanation or measurement for it. For example we can do a null test on something and get a sqiggly line error function, but the debate remains as to whether anyone can hear it, and if they can then whether it is musically meaningful. The trouble is that the ear/brain is what we must satisfy, but it doesn't have a digital read-out or have consistent and verifiable results, and it is subject to error and bias. Beyond a certain point we have to design by ear, and be prepared to alter our belief-sets in response to that.