I am always searching for ground covers that aren't fussy or difficult. Some are not well behaved, and some are even invasive. But here are a few that I like to use to stifle the weeds and tie other plants together in a pleasing manner.
Epimedium, once established, persists well even in dry shade. Its common name is barrenwort, and it has a strong root system that ensures success in zones 5 to 8. ‘Enchantress' is a variety that has dainty pink flowers in spring time that later turn maroon, and fresh green foliage in summer.
Epimediums prefer shade or part shade, but I have one with yellow flowers in the spring where the tree that sheltered it died some years ago, yet the plants continues on happily in full sun.
Our native low-growing Phlox stolonifera grows in zones 3 to 9 and is a woodland plant so does best when it gets shade from the hot summer sun.
Hay-scented fern is a useful ground cover too and will persist in dry shade but does not play well with others, as it overwhelms companion plants. It grows well in zones 2 to 8 but may brown in dry summers.
A native evergreen, Box huckleberry creeps by shallow stems, and because it is a heath, it needs acid, damp woodland soil with adequate organic matter in zones 4 to 9.
Perennial plumbago, commonly known as leadwort, is a versatile ground cover with cobalt blue flowers borne summer into fall and colorful autumn foliage.
Note: Lamium will also grow well in a variety of conditions and has white purple and pink flowers and splashes of silver on the leaves.