It seems to me that we should not assume that we know everything about electrons, their transfer, or all of the elements involved with the transmission of signals through cables. In the relatively short history of human knowledge, and even shorter history of human knowledge about electricity, we are constantly finding new and different explanations (models... approximations, really) of what is going on.
Is it possible that there are aspects of signal transmission that may be somewhat audible in some situations, but are not measurable by currently available and understood methods? I'm inclined to say yes.
To the original point of this thread... Is it possible that these characteristics change with time and/or use in ways that may be somewhat audible in some situations, but are not measurable by currently available and understood methods? I'm inclined to say yes to this as well.
Is it likely that whatever we don't understand has a dramatic impact on sound quality? I'm less inclined to say yes.
But, if history is a teacher, the main thing we should all have learned is that almost everything we think we know will someday be proven wrong or at least overly simplistic.
All of that said, here's what my experience tells me about cables:
1. I once ordered two sets of somewhat modestly priced speaker cables (I think they were like $120ish retail per pair at the 8' length. the company is 'bettercable' but it's not their current line of products). One set went unused because they weren't long enough. Whoops! Anyway, a few months later, I tried out these previously unused pair to see if I could hear a difference between them and the others, which had been continuous use over that period. I could hear no discernible difference. I have not had a chance to try the same thing with interconnect cables.
2. After a bunch of testing and comparing, I think cables fall into three basic categories: basic/zip cord/el-cheap-o, "good", and "too expensive to be worth the marginal gain in perceived sound quality".
I and the folks I can occasionally get to play along with "sam's which-of-these-sounds-better game" seem to consistently be able to identify that the super cheap basic stuff doesn't sound as good as stuff that made with higher quality materials and good quality connectors. We also think that there is maybe some additional improvement with some of the super expensive stuff, but it's really really hard to tell, and very minor. It just seems like the return on investment drops off very rapidly when it comes to cables. I've never been able to hear the difference between $300 speaker wires and $3000 speaker wires on the rare occasions that I have had the chance to compare.
That said, here is what my experience tells me about electronics burning in:
It's real for capacitors and maybe other stuff inside the chassis.
Example 1: My Fisher tube amp definitely sounded different after I put russian PIO caps in (same values, so no frequency response changes). Then, the sound definitely changed over the course of 30ish hours of use. What's that based on? I listened Sunday morning with the old caps, replaced them that afternoon, and gave it a couple hours of listening Sunday night. The change was not hard to identify. I run my amp and tuner quietly in the background as I work each day so by the next time I had a chance to do some real listening, it had maybe 30 hours of "burn in". It was notably different than Sunday night, though not as big of a difference as the initial replacement of the caps.
Example 2: I recently overhauled a Marantz 1060 for my dad including replacing every electrolytic cap and a handful of transistors. I fired it up and was very disappointed with the sound. Bloated mid-bass, dull, sluggish, lacking any sort of clarity, definition or imaging. Sorry dad... I ruined your amp.... But I let it play/"burn in" in the background for several days while I was working. At some point on Thursday or Friday I stopped work and just listened because a MAJOR change, on par with switching between junker speakers and a really nice pair, had happened to the sound. It went from sounding bad, like worse than a 90s aiwa mini system playing a worn out cassette, to sounding really very nice. The bass tightened up, balance across the frequency band was much better, clarity and soundstage were there in abundance. I literally said to myself, out loud, "So this is why people love these amps... hmmm..." It then seemed to continue to improve over the next 10 or 15 hours, though nowhere near as dramatically. To be clear, I do not think the initial change was sudden, but just that I noticed it suddenly.
As a scientist/engineer, I'm skeptical of anything that doesn't have a reasonable explanation, but the scientific process starts with observation... I can't explain what might be happening during "burn in" on the amps, but I can attest to there being a difference in sound.
I can't say I have observed the same with cables.
Is cable burn in real? meh... there probably are some things that happen that we don't really understand, but I haven't heard it, and I have a really hard time believing that they have as big of an impact on sound as almost any other aspect of the overall system.
Klamoss 
