It's critical to select the right carpeting for your stairs, since stairs get a lot of wear, plus the carpeting has to be bent over the edges of each step. A cut-pile carpet is a better choice than a looped pile, as the spaces between the loops will tend to open up where the carpet curls over the stairs in an effect called "grinning." Looped carpets can also snag, especially at any seams or transition areas [source: WFCA].
Density is another factor to consider. If the carpet isn't that thick, you may end up seeing the unsightly backing when the carpet is curved over the steps. One test of the density is to stick your fingers deeply into a carpet sample. If you can easily separate the fibers and feel the backing, it's probably not the best choice for your stairs.
The ideal choice, actually, is a woven wool carpet. Woolen carpets are the most durable, and their woven backing helps keep each piece of yarn in place, which is especially important for stairs [source: Becker]. Unfortunately, wool carpets are pricey.