You don't have to install subflooring in your finished basement, but it does offer several benefits. One is that it keeps moisture at bay. Without the subflooring, the only thing between the ground and the basement is concrete. Water and moisture from the soil can easily seep through cracks in the cement and enter your basement, bringing along mold, mildew, and their associated health problems.
Another consideration would be that subflooring increases the height of your flooring in the event that water does penetrate your basement. A subfloor will give you a few more inches of dry clearance. They can serve as a measure of insulation between the ground and the floor, providing a warmer, more comfortable environment. Having that additional space can also eliminates the damp, musty smell most cement floor basements have.