How important is an audio rack?

It is very important. The best in my opinion is SYMPOSIUM ISIS it is Aircraft Aluminum which is neutral.Wood is wood which is not neutral.This rack will keep vibrations from getting to your componants.

My stuff sits on wooden shelves, but an extreme audiophile I visited had sturdy metal racks; the kind you see in Stereophile. Since his sound was the best I've heard, I know they make a difference. I believe the question "How much"? is related to the depth of one's pockets.

I bought a used Billy Bags rack just cuz I liked the way it looks. It was an upgrade and logic dictated there'd be an improvement in sound quality but I honestly wasn't expecting much. I was very surprised at how much better the system sounded after installation. NOT one of those subtle I-think-I-hear-a-difference-type audiophool tweaks either, it was a clear as day improvement!

"an extreme audiophile I visited had sturdy metal racks; the kind you see in Stereophile. Since his sound was the best I've heard, I know they make a difference."

Maybe, but I'd wager the rest of the gear and the setup as a whole had a lot to do with it.

I guess one would have to switch racks and a/b compare to know for sure.

Another important consideration in an audio rack, IMO, is that it is open on all sides, so there is plenty of air, and your components do not overheat. I use the Sanus Natural Foundations rack, which has glass shelves. They are very sturdy, and I have no vibration problems.