Which Cables Are of Most Importance?

My guess is that it would vary from system to system. I personally have noted the biggest differences with ic's and speaker cables. Power cables do make a difference but I note the improvement in the better ones in lowering the noise floor of the system not in any substantive way in the manner of a good ic or speaker cable. ICs and speaker cables have more impact on different parameters of the presentation although in many cases, most I would say, the differences can be quite subtle. YMMV. HDMI, no experience with them. I do agree with Elizabeth though, the umbilical is the most important.

Rrog,
The point of wire importance is always floating. In my rig the link between amp/preamp is less important than TT --> phonostage.

Power cords by far.

Power Cords by far.

i put a morrow map-3 ac cord [600 bucks with upgraded wattgates] on my 300 dollar emotiva preamp and it has transformed my system. the soundstage is extremely open and pleasing to my ears. i suspect i will be advised i should have just bought a 1000 dollar preamp of some flavor but so it goes in my world.