Basements present wall framing issues that the other rooms in the house do not have. For example, when you are determining where to put the wall frames in your basement, you will have to work around furnace duct work and plumbing running across the top of the basement. In most other rooms in the house, the ducts and plumbing are not an obstacle to framing a wall. Spend time planning your wall placement to prevent boxing in important house elements that you will need access to from time to time.
Basement floors tend to be uneven, which creates issues with building wall frames that have to compensate for the pitch in the floor. If your basement floor is one inch higher at one end than the other, your wall frame will have to be built an a slight angle to compensate for it. In some basements, the area where the floor meets the walls creates a small rise that makes framing a wall directly to the concrete basement wall difficult. To combat this, you need to include a space between your finished wall and concrete wall. which will decrease your usable floor space, but will insure the stability of your walls by placing them on the flat concrete floor.
Basement walls tend to gather moisture, whether they have been waterproofed or not. Moisture on concrete walls that ends up absorbed by the fiberglass insulation and drywall of your framed walls can cause a mold problem in your basement that could spread throughout your home. Put a vapor barrier between the concrete wall and the fiberglass insulation to help combat moisture. A vapor barrier is an additional layer of insulation, but is significantly thinner than fiberglass insulation and is designed to prevent moisture buildup.
Over time, the concrete walls and floor in your basement may begin to develop cracks. When you put wall frames on your basement concrete walls, you eliminate the ability to see cracks when they start and prevent further damage to your foundation. If you put wall frames up on your concrete walls, have a professional contractor survey your foundation annually to check for any cracks that may be starting.