Yes they do.  I’m not here to advocate for any particular brand but I’ve heard a lot and they do matter. High Fidelity reveal cables, Kubala Sosna Elation and Clarity Cable Natural. I’m having a listening session where all of them is doing a great job. I’ve had cables that were cheaper in my system but a nicely priced cable that matches your system is a must.  I’m not here to argue what I’m not hearing because I have a pretty good ear.  I’m enjoying these three brands today and each is presenting the music differently but very nicely. Those who say cables don’t matter. Get your ears checked.  I have a system that’s worth about 30 to 35k retail.  Now all of these brands are above 1k and up but they really are performing! What are your thoughts. 
If cables do indeed make a difference, then am I to assume they all sound differently? If there was a level playing field blind listening test with say 5 high end cables. Would anyone be able to say what make of cable is playing? 
Of course they make a difference. Or else there wouldn’t be a cable industry. My question is, What are the makers of $12,000 cables doing that the $2,000 cable makers are not? The differences are certainly not in materials, the materials used are not that exotic. Is it not possible to buy a $12,000 pair of cables and reverse engineer them? And mass produce them for $2K? I wonder? 
@gawdbless, if you wanted to be really naughty you could also throw in a straightened coat hanger, some $1 per metre oxygen free cable and then see what happens.

Strangely enough, no high end cable manufacturer ever seems game for the challenge. Not now, not yesterday, not tomorrow.

@nonoise, seriously, it's time we moved on to types of connector, banana v bare wire v spade, spring clips v screw threaded binding posts, tightness of connection, and perhaps going the whole hog and rewiring the entire domestic audio chain with $250,000 of wire.

I get nightmares when I recall the cheap spaghetti like wiring loom at the back of the mixers and under the desk at this studio where I worked some 20 years. And yet, guess what? We got some lovely sounds coming out of that setup. At least until we switched from vinyl, minidisc and CD to PC based Mp3 files.

Never did find out the bitrate but I doubt whether they were over 128kbps. Perhaps not even that. They seemed more concerned with using Audacity to tidy up recorded broadcasts.
I think some of us are our own worst enemy and won't take components (including cables) seriously unless they cost a certain amount. The manufacturers know that and price stuff accordingly.