I run across many homes that have crawl spaces instead of a basements, either under the whole house or under additions built on after the original house was built. This was done for a number of reasons, most usually cost or how high the water table is. Some are built with a concrete floor but most are just bare dirt and/or gravel. Although this is a less expensive way to go, it can cause bigger problems down the road if not done correctly.
The original rule of thumb for the crawl space dealt with ventilation. It did not matter what the base of the crawl space was as long as the ventilation was correct. This was later changed. Now the experts recommend no ventilation. They recommend the owner create an environment where someone could live in the crawl space. Obviously the experts do not think someone would live in the crawl space, but if the air quality, temperature, and humidity are no different than the living space, there should not be a mold issue.
A concrete pad will help control the moisture in the crawl space. Dirt or gravel, however, will not stop moisture from evaporating into the crawl space, which can cause a mold issue on the subfloor or possibly in the living space. In this situation, a plastic membrane should be installed. This should be attached to the walls of the crawl space and sealed at any seams, including any supports in the center of the crawl space. A thicker plastic (such as 6mil) should be used to help avoid tears when someone needs to use the crawl space. In certain situations, the height of the crawl space will make it impossible to work without taking up the flooring above it.
Once the flooring of the crawl space is set, a dehumidifier should be installed. This may be difficult if there is no drain to empty into, so a condensate pump may need to be installed to pump into a drain or piping. If there is a full basement attached, an opening connecting the crawl space to the basement will allow the dehumidifier to operate in the basement while dehumidifying the crawl space.
Conditioning the air in a crawl space will reduce the potential for mold, and it will also make your living space seem warmer in the winter months due to less humidity in the air rising up from the crawl space. If your crawl space is very wet, these changes are highly recommended. If you are getting mold on items in your living space, this could be the biggest culprit. A trained professional will be able to help you determine what would need to be done.