It has been very hot around here with no rain in sight really, so wet basements probably have not been on your mind. But with this humidity you could still have trouble in your basement.
Hot and humid weather just increases the humidity and moisture in your basement. High humidity can lead to mold and mildew growth. Depending on the severity, conditions can lead to rot, structural damage, premature paint problems, and health problems.
High indoor humidity caused by normal activities of everyday living, such as showering, cooking, and drying clothes, can also be a source of your problem. A damp basement is commonly caused by moisture migrating through a concrete foundation. There may not be a sign of any leak or standing water, but the moisture evaporates, increasing indoor humidity. Another common cause is condensation on the cold concrete walls and floors during humid months.
There are only two possible ways to eliminate condensation: heat the air or pull the moisture out of it. Obviously heating your basement to match the outside temperature is counterproductive, so the only real option is to dehumidify.