Flooring choices for the basement are limited simply because the room is below ground level. While a carpet may be your first choice for covering the floor of your cool basement, you do not want to have to deal with mold and mildew. This may occur if you have a water problem, in addition to the hassle of a perpetually wet or damp carpet. If this is the case, you should look for basement waterproofing
options to solve that problem.
However, this does not mean that carpets are not suitable choices for all basements. If you are sure you have a dry basement, there’s no reason why you shouldn’t get a carpet.