I have found that cables make a significant difference in the sonics, this after 33 years of having used them. I could fairly easily hear the sound of the cables in my system, but I do want to say that I started out with WATTs in 1986, so hearing speaker cables/interconnects was very easy with WATTS/Goldmund/Jadis/Convergent gear.
The tricky thing is determining if the cable is exposing flaws in the preceding components, or masking previously unheard flaws. That's the part that - after the burn in period, which for Nordost and Shunyata cables, is around 3 weeks of non-stop playing (and that's a pain if it's the speaker cable, because unless you have a cable cooker, you are going to have to play music. And it's not my imagination: I was an editor for the late, lamented Fi Magazine, and I'd have to help set up equipment and listen, and given what my boss had (Grand Slams, Rockport, Jadis, Transparent cables), I could hear any change, such as removing the cables from touching an AC cord when he had a demonstration of his system at his home in Marin County (where the rich don't itch!) in front of **** Bel of Bel amps, and the Managing Editor - at the time - of The Absolute Sound, Sallie Reynolds and my mentor, Tom Miller. And the difference between removing an ac cord from the vicinity of the cable was heard instantly by all (the upper midrange edginess disappeared). So, if you've got cables touching each other at home, you're not even going to hear the differences in cables, and I suspect that this is, in large part, why so many people disparage high end cables. I've been to stores in New York, San Francisco, Boston, Hartford and it was appalling how many retailers paid ZERO attention to how their cords touched each other. It made me angry that they were actually causing the equipment to operate at sub-optimal levels. And I see it in a store here whenever I go in (which is why I don't go in much any more: I can barely keep my fingers off the cables to re-arrange them, but I can tell you this: I have free run of that store, so one day, I re-arranged the Nordost Odin ac cables to be as far away from the signal cables as possible. The difference was very obvious to me - AND them. But they said it was 'too much trouble' to keep components set up correctly. Now, THERE'S a good 'sales attitude' for ya.)
For non top-of-the-world cost cables: Alpha Core Goertz Divinity and MI-3 cables are excellent. They image well, have a very good tonal balance and extremely low noise floor. TAS, back in 1998, tested them both, and Harry found them so close to Nordost, he wasn't sure he could reliably tell which was which (except, he said, the Goertz had better mid-bass). After he switched to vinyl, he was more able to hear the differences reliably. Also, Nordost Heimdall is very good (not saying this is cheap. The Goertz was what I'd call 'reasonable' after having purchased Valhalla back then (2004) and found the Goertz indistinguishable from the Valhalla. And I had it for months, as I was writing a review on it for Ultra Audio.
Expensive cable does make a difference, but others are right: you must hear them in your own system (and keep your bloody hands off of them once you have them optimally positioned. Even moving them around will cause the sound to blur a little (use a vocalist, and female works the best, and you'll hear Streisand, Garland, Fitzgerald lose a modicum of expressiveness. Not heard to hear on unprocessed vocals, unlike anything after 1973). And allow them to "settle" for 2 hours before playing music. (Try not to argue with this point until you've actually done it, okay?) Or maybe one hour, but Shunyata and Nordost cables? It'll be two hours before the optimum sound emerges.
And yes, the synergy counts, but more many, it's compensating for other things they bought before trying out cables.
And don't even ask about power cords, because yes, regardless of what you hear, they change the sonics. Shunyata's current Alpha line is wonderful, but slightly less perfect in the upper bass/lower midrange, although they will just say, 'if you want a warmer sound, the CX is good..." The problem with that is that the CX line casts ITS coloration over the entire spectrum, so everything sounds warmer. Don't expect to listen to Janis Joplin and Big Brother and hear the guitars scream and growl: they'll sound warmer with a CX cord, and more true with an Alpha, but the Alpha will still leach out some of the natural color of a guitar or cello.