To begin with, I agree with the post title, "Yes, cables do make a difference -- regardless of price..." The types of cable commonly used in an audio system are speaker cables and interconnect cables (I'll avoid discussing power cords here, but as a learned friend says about them, 'Wire is wire'), but each type have different performance requirements, although the factors that affect that performance are similar, in many cases. I'll discuss that a bit, but I will state emphatically right now that there is no cable available (either manufactured or fabricated) that will sound good with every system, regardless of cost.
Starting with speaker cables, their task is to carry large amounts of current (power) from a source (amplifier) to a load (loudspeaker). Although it sounds simple, there are some significant variables associated with it, namely the source (output) impedance of the amplifier, and the load (input) impedance of the loudspeaker. Although in a solid-state amplifier the source impedance is typically near zero (i.e., less sensitive to loading), tube amplifiers use output transformers whose typical source impedance is about 2 W or so, (considered high impedance, in this case), the load impedance of a loudspeaker is relatively high (e.g., 4 to 8 ohms) and varies due to frequency. So what works best? Several years ago, a major audio magazine conducted double-blind tests of speaker cables and had the courage to publish the names of the manufacturers. (That article is virtually impossible to find on the internet today, effectively censored.) One of the highest rated 'speaker cables' was an extension cord from Home Depot! After reading this I rushed out to my local store and bought one. Consisting of 8 AWG individual conductors, it certainly looked impressive when I cut the plugs off to install spade lugs on it. I anxiously connected them between my amplifiers and speakers with the anticipation that I was going to have great sound. Upon listening, however, I found the sound to be fat and tubby. Given that my speakers at that time were Carver AL-III ribbons, their design normally provides detailed and crisp sound. What a disappointment!
With a background in electrical measurements, I subsequently measured the Home Depot cables and discovered that besides their massive girth, their series inductance was very high. Since their reactance (expressed in ohms) is calculated using the formula, RL = 2pfl (not to mention that inductance increases with the physical length of the wire), it's obvious by inspection that resistance rises significantly with frequency, impeding the transmission more as the frequency increases, causing an imbalance between the bass and treble frequencies reproduced. In the case of the ribbon drivers of the AL-III, their characteristic impedance is relatively flat to 20 kHz, but an electrostatic panel, for instance, can drop to 1 ohm or less at 20 kHz, further impacting the sonic qualities associated with high inductance. In general, I have found that the lower the inductance, the better a speaker cable sounds, although it must be of adequate size to carry the intended current. I should also mention that much of the wire available now (especially from China) is not pure copper (Cu), but a mix of copper and aluminum (Cu/Al), due to cost, and it's performance is not as good as pure copper wire.
Like speaker wire, interconnect cables are also impacted by the source and load impedance of the components (e.g., preamplifier, CD player, etc.) they are connected to, but in a different way. The source and load impedance of most audio components are relatively high, compared to those associated with amplifiers and loudspeakers. For example, the line inputs (unbalanced) of my current preamp are 20 kW (relatively low, in general, however), and the source impedance of most components are also likely similar, although typically unspecified. The problem that arises in this case are those of parallel (shunt) capacitance associated with the interconnect cables. After listening using the several different interconnect cables that I owned, I subsequently measured their capacitance. Regardless of cost, I found that those with the lowest capacitance sounded the best.
If manufacturers and reviewers both wanted to provide the best information to consumers, in my opinion, they would state the electrical specifications of the cables they sell and review. For example, Stereophile® prides itself on the fact that it provides measurements on the audio components it reviews, but never (to my knowledge) have they measured the electrical characteristics of the cables they have reviewed. I suspect, however, that a request for such information from a manufacturer would be met with a response that that information is proprietary. A few dealers I have heard of actually have 'loaner' cables that customers can borrow to try in their own systems, but those dealers are few and far between.
Given that we all have different components in our audio systems, with differing source and load impedances (and operating characteristics, when it comes to loudspeakers), suffice it to say that when it comes to cables and their performance, I will reiterate that there is no 'one size fits all.' That said, it's just as obvious that no manufacturer can make the claim that their cables are the best (perhaps the most expensive). I have given some typical characteristics that I have found work for me and likely will for others, but ultimately, each individual will have to make up their own mind using their own ears.
Good Luck!