Of course they do, just like everything else, power cords included (big time).
Do not listen to the naysayers. All they do is repeat stupid stuff they have read in 1973. Maybe they once tried some cheap-@ss Monster Cable (LOL) and didn't hear a difference (no kidding?). In a decent system, swapping cables can be as audible as swapping amps, and sometimes more audible than swapping DACs. Of course, going from multi strand OFC 16 brand A to multi strand OFC 16 brand B won't necessarily give a huge difference, sometimes it does, sometimes not. But compare your favorite lamp cord to a quality, well engineered cable, be it solid core, ribbon, whatever, different materials, and the difference will be very audible.