Stonecrop (Sedum) is quite shade and drought tolerant. Several leaf types and colors are available. Flowers range in color from yellow to pink and white. The most shade tolerant is Sedum acre, often sold as Golden Sedum. Sedum is quite attractive growing in rocky areas and small pockets in rock walls.
Native Creeping Potentilla (Potentilla verna) grows only an inch or two high and tolerates moderate shade well. It has yellow flowers in the spring with intermittent bloom during the summer.
Lamium maculatum has variegated green and silver leaves and white, pink, lavender or crimson flowers. Lamium flowers from early spring until fall. It needs plenty of water and does not grow well in dry areas. It is easy to keep to a confined area.
Creeping Jenny (Lysimachia) is another shade tolerant ground cover which needs plenty of moisture. It grows well in wet areas such as next to a pond. Creeping Jenny grows only 2 inches tall with yellow flowers in late spring. A yellow leaf selection is also popular.
Our native Kinnikinnick is somewhat shade tolerant and drought tolerant. It grows about 4 inches high and stays evergreen most winters.
Vinca minor is a quickly established ground cover which grows in sun or shade. It needs some confinement to keep it from growing into unwanted areas. It produces attractive blue flowers in the spring.