Many viewers ask if they can put carpet over a concrete floor. The answer is a qualified Yes.
There are three different concrete floors to consider: those in upper floors of the house that are always high and dry, those in the basement that may possibly run into moisture problems and those outdoors that will definitely get wet.
When you have no moisture problems to consider, the only thing that you have to take care of is the mechanical ware of the back of the carpet that would happen if it was allowed to rub against the concrete. Two solutions: glue the carpet down or use an under pad to protect the back. If you choose to use the soft under pad, be sure you have a carpet that is compatible with such an application because many are very stiff, designed to be glued down, and they will simply crack and break if you bend them every time you step on them.
On a basement floor you may need to test to be sure there is no moisture that can come up and give you future problems. Tape a piece of transparent plastic on the floor. If it collects moisture on the top of the plastic you must reduce the humidity in the basement before putting down carpet. If it collects moisture on the concrete side, you need to find the source of the water and solve it (landscaping around the house, sump pump etc.) If it remains dry, then you can install as on any concrete floor, except do not use under pads that can absorb moisture. The best will be quality rubber pads, not foam pads. One rubber pad that sounds like a great recycling idea is a 100% rubber under pad made out of recycled car tires. I cannot recommend it, just put your nose to it yourself and I don't think you want that "new tire showroom" smell in your rec room.
Outdoor carpets require special adhesives and special outdoor carpet capable of withstanding water and ice as well as mold and moss. The surface should slope in such a way as to naturally drain water off of the balcony or porch. Remove any spalling or chipping concrete and make the surface flat and smooth with patching compounds. Here we know that this whole assembly will eventually get wet, but it must be completely clean and dry when applying the adhesive -- and you must protect it from rain for at least 3 days. As soon as the carpet is placed into position, pass over it with a heavy roller to force the carpet into good contact with the adhesive.