When I started planning my basement, I was concerned with having the flooring sitting right on top of cold concrete. Even with an underpad, you'd still feel the rock-like hardness underneath your feet. I decided then that I would build a subfloor. The standard way of building a subfloor involves laying pressure treated 2x4's on the concrete and screwing floorboards on top. Flooring material like carpet can then be installed on top. However, this means that I'd lose over 2 inches of vertical height.
I then started looking into alternative solutions. You can get a dimpled plastic material that's rolled out on to the concrete and then cover with 5/8" plywood floor boards. I was considering using that when I discovered Dricore. Dricore is a 24"x24" tile that's 7/8" high. On the bottom is a plastic layer with a waffle-like pattern that allows air to circulate and on top is random wafer board. The tiles are simply floated on top of the concrete floor and attach to each other in tongue-and-groove fashion. I was able to install the entire basement in two weekends.