To choose bedsheets that won't pill, you have to pay attention to the quality of the fabric as well as the construction of the sheet.  Look for bedsheets with a high thread count, as this indicates a tighter weave and helps prevent pilling.  Also consider the ply count of the fabric, which refers to the number of yarns that are twisted together to form a single thread.  Single-layer fabrics are generally smoother and less prone to pilling than multi-layer fabrics.

The twill weave is characterized by an over two, under two pattern. It leaves behind a distinctly diagonal design and is typically wrinkle-resistant due to the thickness. Twill woven sheets are prone to shrink more than those with a sateen weave but are also often times more affordable.