Creeping juniper is a low-growing evergreen that will not overrun steps or stairs. Blue rug jupiter -- J. horizontalis 'Wiltonii' -- stays under 8 inches tall but spreads slowly to 6 feet. It is easy to maintain and keeps its blue-green color all winter.
Moss pinks -- phlox subulata -- is a flowering groundcover. Phlox has evergreen or semi-evergreen foliage but it is grown for its abundant spring flowers. Suitable for sun or partial shade, pinks form dense, 6-inch-by-2-foot mats that that cascade over walls and rocks.
Irish moss -- Sagina subulata -- forms a dense, mossy mat. This plant thrives in deep, moist shade. Tucked between the crevices of stone steps, Irish moss creates a natural weed barrier.
Do not use English ivy near steps. English ivy is used as a ground cover and trained to grow up walls but its roots can damage the mortar between bricks.