I usually unplug mics and such, but most of gear stays wired up ( i use a patch bay so no way in hell would I unplug it every time). Actually, now that i think of it, I leave my triton plugged in to my avalon DI's, so some stuff stays plugged.

As for mics, especially nice ones, I would put them away after use for sure- just leave the shockmount on the stand, and drape the cable- it only takes 5 seconds. Dust is not good, nor is the chance of knocking it over. I actually bought a couple road cases for my mics, and custom fitted the foam- they're not too pricey and waaayyyy worth the investment- the cherry wood box that came with my blueberry looks great but I doubt it would survive anything other than polish.

Welcome to RO!

There shouldn't be any damage that can happen with leaving cables connected or connected on only one end other than that they can sometimes become antenee for picking up noise, EMF, RF and other audio junk. This of course assumes you'll never encounter any wild surges of voltage or current through them.

My rule of thumb is, can their be damage caused at any time inadvertently by leaving the cables connected?

Usually any cable that is plugged into the front of my stuff, gets disconnected so I won't accidentally step on it and pull it out or break it or the input jack. Gear that is in the rack and cables routed to the patch bay stay connected.

Oxidation can build up after time so it is a good idea to go through all your connections and reseat them once in a while.

As for nice condenser mics, dust and deterorating foam in some mic cases can damage the diaphragm. I keep mine either in their original cases wrapped in a plastic bag or on the stands sometimes. I try to bag them with a plastic sandwich bag (a clean one, not a used one that you got some weed in) or some type on nice vinyl or cloth bag