Nice one, Joel! This is bound to trigger some "robust debate" among the masses...
My R0.02 worth:
Firstly, the question is not a simple one that can be answered with a binary Yes/No type response - there are a number of aspects to be taken into consideration. Firstly, lets agree on the definition of "equipment stands" and identify those aspects which are specifically excluded:
An audio equipment stand provides a number of shelves intended to house audio system electronic components such as source components and amplification. It is NOT intended to house/support loudspeakers.
The next aspect should be to categorise and group the areas of potential benefit provided by an audio equipment stand:
a) Optimising equipment "environment"
b) Optimising the sound quality of the "system"
c) Isolating the equipment from external vibrations
d) Minimising contra-arguments from SWMBO
The first area should not provoke too much dissent - audio electronics generate heat which needs to be dissipated to permit the components to function within their designed operating temperature range. If this heat cannot be adequately dissipated, then the temperatures will rise - the degree of rise being determined by: firstly, the amount of heat generated by each component; and secondly, the heat dissipation rate provided by ventilation (natural or forced). A well-designed audio equipment stand that has been matched to the components configured will provide adequate clearance and adequate ventilation and, thereby, permit the equipment to operate well within optimum operating temperature ranges. In addition to the possibility of damage from over-heating, components that run too hot can also sound different from when they are running at optimal temperatures - so a stand can, via decent ventilation, detract less (nice turn of phrase there, Joel).
The fourth area (yep, I'm skipping ahead to handle the easy bits first) is not quite so straightforward, as it depends to a large extent on the aesthetic tastes/preferences of the "significant other". Usually, the reaction will be either "I love it!" or "I hate it!" - beauty is, after all, in the eye of the beholder....
The third aspect of "insulating" the equipment from - typically floor-borne - vibration depends largely on the combination of the floor type and stand-type. A sprung and suspended wooden floor will render any floor-standing equiment stand prone to the negative effects of floor-borne vibrations. In cases like this where a suspended floor exists, the equipment rack should preferably be wall-mounted. On any solid and "dead" floor, a decent equipment stand - ie one that is rigid enough and does not "cross-pollenate" vibrations from one component to another as a result, will "detract less from the sonic performance" of the system (much better wording than "improve" which always sparks off a mild flame war or two).
Coming back to the second category (although touched on in the above paragraph), this is an area where it is probably worthwhile examining under different categories of component. A turntable, for instance, demands a very high level of mechanical isolation to prevent positive feedback from detracting from the sound (there's that word again..). Just how much real difference mechanical isolation can make for the benefit of amplifiers and other non-mechanical source components, is - from my perspective at least - not quite so clear-cut. The transformers used in amplifiers do generate mains frequency level vibrations which are more likely to cause problems elsewhere, so the benefit of isolating amplifiers is most likely to accrue in other areas than in the amplifiers themselves.
Overall? I concur with your belief that a good stand can and does make a positive difference to the sound quality of an audio system - particularly if a turntable is in the configuration - by "detracting less from the performance" (love that phrase...).
Whether or not a stand can make as much difference as claimed by some manufacturers, is another matter altogether...
