This is a subject that we don’t like to talk about, No one does. As a professional working in basements for 25 years I have to bring it up. There is mold in basements, even if you can’t see it. Sometimes you can smell it but still can’t see it. In this case if your basement is not finished all that is needed is air circulation and a dehumidifier. Always use a dehumidifier in your basement, finished or unfinished. Then a good thing to do is to not close your heat ducts. A lot of people close them off and when the furnace runs the basement doesn’t share in the circulation of air. Also make sure there is a return air cutout into the furnace cold air side. This gets the air off the floor and into circulation. Then install a good quality filter system, something rated for mold.
If you spring a leak in a unfinished basement get it fixed as soon as possible by a professional and keep the floor dry till you can get it fixed. If you follow this, you shouldn’t have a problem.
If you spring a leak in a finished basement behind the walls the problem is not so apparent right away. Sometimes it is a year before you can figure out there is an actual leak. Almost always the carpet gets wet after a rain. Most people don’t know this but the mold will grow in the carpet as soon as the first time it gets wet. After a year of on and off leaking you should figure on trashing the carpet and deodorizing the basement. Again it pays to call a professional right away.
The following picture is a mold or fungus growing on a door jamb and casing and carpet. The leak was let go for a while.
This next picture is of what looks like standing water but actually the water was drained and what is left was a 1/2 inch thick gelatinous layer of liquid black mold. When things get this bad I recommend calling a mold abatement contractor. These firms are required to have a special license. Make sure they have one. Using negative air pressure is also recommended during the clean up.