A good quality carpet pad is a smart investment.  It adds considerably to the Beauty, Comfort and Durability of your carpet.   Often, retailers will include a pad in the price of the carpet.  Before immediately agreeing to that pad, ask about the options available.  A low-grade, low-density pad just doesn't support carpet very well. If a pad doesn’t provide adequate support, the carpet might wear out prematurely. A pad that is too thick or soft can actually reduce the life of your carpet. In general, a thinner (no more than 7/16"), denser pad will prevent undue wear on the carpet.

Padding is described at retail in terms of pounds, e.g., 4 lb., 5 lb., 6 lb., 7 lb., etc.  The term ‘pounds’ here refers to pounds per cubic foot so a cubic foot of 6 pound pad weighs 6 pounds. [A cubic foot of padding is sliced into 1/2" pieces, giving you 24 equal slices.  With a 6 pound pad, that would mean that each slice would weigh 1/4 lb. per slice.]  An 8 pound pad weighs twice as much as a 4 pound pad for the same sized piece of padding. 

Rooms subject to heavy wear will require a dense pad that is less susceptible to deforming over time, while rooms with lighter use can get by with something softer.

Carpet construction affects the choice of proper carpet padding.

• The most common type of foam carpet pad is rebond pad, used by about 80% of the industry. Rebond is made from scraps of foam used in furniture and bonded together. For rebond pad, most carpet manufacturer warranties generally require at least a 6-pound pad for cut pile carpets and 8-pound pad for looped carpets.
• Fiber pads are made from either natural or synthetic fibers. Synthetic fibers such as nylon, polyester, and polypropylene are now widely used because they're cheaper to make. Fiber pad can even be made from recycled carpet.  Loop style carpets typically use a fiber pad.
• Rubber carpet pad is made either flat or in a waffle pattern. Rubber is a thin, firm pad so it is frequently used under Berbers or in commercial applications.

Carpet manufacturers have minimum pad recommendations for each carpet so ask the retailer what the manufacturer recommends. Follow the manufacturer's recommendation.

Padding is ultimately your decision unless restricted by building code.  To help in your decision, consider placing a sample of the carpet you like over a sample of the pad recommended by the manufacturer.  Step on it to determine if you like the feel underfoot.  Don’t forget to try additional pads offered by the retailer before making your final choice. 

Note that medium and higher density pads generally improve the wear performance of carpet.

The Carpet and Rug Institute, the carpet industry trade association, publishes recommendations for selecting padding.