The traditional definition of "organic", used by chemists, is that a substance is organic if it consists of carbon compounds. "Organic chemistry" is the study of compounds of carbon.
Most sand you find in deserts consists of silicon dioxide (quartz), and therefore can be classified as "inorganic".
Many sands on ocean beaches, particularly the very white ones, have big contributions from ground up seashells, corals, and diatoms. Calcium carbonate is a big ingredient in seashells, and so beach sand has carbon compounds in it after all. Cacium carbonate dissolves in water, however (it's one thing that makes "hard" water hard), although ocean water is already saturated with dissolved calcium carbonate, unable to take any more. There may be other carbon compounds in some sands, like silicon carbide.
Sand on the beach may have other stuff in it, like little bits of seaweed, driftwood, fish skeletons, shells, and lots of other organic things (many of them still alive!).
The other very common use of the word "organic" comes from the food biz. A food is called organic if it has been grown without the aid of artifical fertilizers, pesticides, or herbicides. Even if a food doesn't satisfy these requirements, it probably still contains carbon compounds! Very fine sand may be added to some foods for non-nutritional reasons. I have a jar of paprika powder at home which lists, among its ingredients, "silicon dioxide" (sand), added in order to keep the paprika from caking up in lumps when the humidity goes up. I suppose if the paprika were grown in accordance with organic farming rules, the addition of the sand probably wouldn't keep the "organic" label off of it.
(published on 10/22/2007)