We are refinishing our basement and have not yet decided what to do for the floors. Part of the basement will be tile, and we are all set. However, the rec room side is going to be carpet. The basement is dry, and we have never had any water or moisture issues.
Some research has said to simply lay carpet like normal, with a thinker pad on the concrete. While OK, I am worried a little about the coldness, a vapor barrier, and the comfort level (too hard on concrete). One carpet guys said they make special pads that are vapor or moisture proof and will not have mold issues and are made for concrete floors.
Other people has said to lay .5"-1" foam board down, and then install plywood on top of that. That would help to insulate, make it feel like a normal floor, and provide a good moisture barrier) But this would cost more in labor and materials, and cut into the height of the room (it is 7'8"). And although we have not had water issues, heaven forbid if we did, this would be a major pain to rip it out.