The best flooring to put over concrete includes epoxy, linoleum, cork, laminate and vinyl. These materials resist water, mold and mildew. Most feel good to walk upon and come in different patterns and colors. Linoleum, cork and vinyl are also easy to install.
Linoleum and cork are also inexpensive. Materials that are not as highly recommended include porcelain tiles, stone, polished concrete and carpeting. Carpeting is basically not recommended for a concrete basement floor, for the concrete inevitably absorbs moisture from the soil around it, and the moisture damages the carpet fibers.
Epoxy is expensive, but is so water-resistant that it forms its own vapor barrier. It is the best material for a basement that is at risk of flooding.