Basement floors are notorious for becoming damp, and moisture will ruin a floor unless necessary precautions are taken. If you do take those precautions though, you can put down many types of flooring, including vinyl, ceramic tile, engineered hardwoods, laminates, or carpet. Flooring experts generally recommend against installing traditional strip or plank hardwoods below grade.
Woods: The ideal way to put down a wood floor over concrete that is subject to dampness is to first put down pressure 2-by-4 inch "sleepers," or lengths of wood, on the floor that are spaced 16 inches apart on center. Cover the sleepers with 6-millimeter plastic and then lay down 5/8-inch plywood. Cover the plywood with 15-pound roofing felt, and then install the engineered or laminate floor. Engineered wood floors may be nailed or glued to the plywood subfloor.
Laminate: Laminate floors, which may be tongue and groove or snap-together, are "floating" floors and not attached to the subfloor. If the concrete subfloor is always dry, however, laminate floors can be placed directly on the slab.
Carpet: Carpet can be laid in the same manner as woods. It’s important to put down padding as well to protect it from any kind of mold or mildew buildup from moisture, as well as to help with the concrete beneath.
Vinyl tile: For vinyl tile, skip the 15-pound felt and apply mastic directly to the plywood. A thicker grade is a good idea if the concrete is uneven, to keep people walking on the surface from feeling the bumps beneath the tiling. Vinyl plank flooring, which appears wood-like, is another option that makes for easy installation and repair when needed.
Ceramic tile: For ceramic tile, nail cement boards to the concrete floor with concrete nails so they won't move, then apply mastic, tile, and grout. If you feel that despite all precautions the basement floor may get wet, put down 2-by-4-inch sleepers, cover with plastic, and then install the plywood as the subfloor.
Rubber tile: Usually used for garages, these can be laid as tiles in a basement. These lock together atop a moisture barrier, and since they’re inorganic, they risk less of a chance of mold than other types of flooring. They will need to be removed occasionally to let the concrete floor dry, but they are very comfortable to the feet.