Do you consider cables to be a "component" of your system?

Absolutely YES YES YES

Yes, cables are definitely a vey important element of MY system. They can make or break a system in my opinion, and so can anti-vibration platforms, power conditioners, and so on. You really don't need to have golden ears to hear what they do - in my system. I've enjoyed a tremendous (yes, TREMENDOUS) upgrade of resolution, openness, pace of said system after replacing the whole cable loom. It certainly brings as much an improvement as changing the amplifier(s) for more expensive ones, or the DAC. And it costs less. It seems to me a lot of audiophiles just go through an awful lot of component swaps without ever trying to get the best out of them, wasting time and money, when very often all that was needed is a little attention to surrounding devices and cables.

Now of course there are systems where the improvements might be more subdued, and where you mIGHT need more concentration to hear the differences, which may seem too subtle at first. 

Try it with a high sensitivity, fully horn loaded system like mine, and you'll be shocked. My explanation for that, is when you use 100dB+ sensitive speakers, at normal domestic listening SPLs, the signal travelling through your devices stays really really low, uncomfortably close to the plane where distortions and noise induced by external perturbations (spurious vibrations, EMI, RF, mains noise...) reside. That doesn't make it a "better" system, it's just a characteristic of very high efficiency, and is more often than not a plague rather than a blessing. Yes, in my system, you clearly hear everything, from the type of cable used to the platform where the DAC and the transport reside. It's absolutely not "subtle", rather dramatic in fact. 

That being said, even in a conventional system cables are important and yes, I believe ears can be trained for critical listening, there is absolutely no doubt about that.  

Wow, all of the deniers are here after they were asked NOT to spout off with their negative comments. Please read the original post, it clearly states “Please, please, PLEASE don't tell me that cables don't make a difference. I disagree and there's nothing you can say or do that will change my mind, so save it for another thread, please.”  What part of that don’t you understand?

@d_joudrey I find it amazing is that you read any review, premier, report from an audio show. every speaker, amplifiers, streamer, DAC manufacturer is using upgraded cables, interconnect, power, speaker, tonearm, and enhanced internet switches and connections, or fiber. Many of these manufacturers have no connection to these other manufacturers. So why would the do this?

Simple to maximize the performance and experience of the reviewer, customer. Because they make a difference. If it truly did not then they would use the cheapest crap on the planet.

I’ve tried cables that made more difference in sound than swapping DACs (the two DACs being relatively similar in technology and price, but showing their own subjective differences nonetheless).

I own so many different cables I could easily alter the tonal and spatial characteristics of the system by changing the cable loom, and not by a small degree. So yes, in my experience cables are definitely components that have to be chosen with as much care as the rest.