If shade trees are the ceilings, and hedges and shrubbery are the walls, then turf and other groundcover plants are the floors of some of our outdoor living spaces. Except for turf grasses, most groundcovers are not as useful as hardscapes like pavement and decking, but they perform other functions in areas that do not get such use. Groundcovers inhibit weeds, erosion, dust and mud.
Turf grasses used for lawn are of course the most popular groundcovers, and are a separate topic from other groundcover plants that grow over unused or lightly used ground. Because they need not tolerate traffic, these other groundcover plants need not be as resilient, or as flat as turf grasses are. They can be perennials, vines or low sprawling shrubbery. Most, but not all are evergreen.
Groundcover plants work something like mulch, although most want to be watered. They inhibit weed growth by occupying the space that weeds want. Many hold soil together with their roots. They may seem like they would compete with other plants, but groundcover plants insulate the soil, which makes it more comfortable for other plants. Many retain more moisture than they utilize.
Gazanias and iceplants are two of the most popular perennial groundcovers. They tend to replace their own growth regularly as old stems decompose below new growth that spreads over the top. They therefore do not get very deep. Some gazanias eventually develop bald spots. When they get trimmed around the edges, the scraps can be plugged back into bald spots as cuttings.
Cultivars of myoporum, cotoneaster, ceanothus, rosemary, juniper and other low and sprawling shrubbery that make good groundcover must not be confused with cultivars that grow as upright shrubbery or even trees. There is a big difference between creeping myoporum that stays less than a foot deep, and shrubby myoporum that can get almost thirty feet tall! Also, vines used as groundcover, like ivy and honeysuckle, should be maintained as such, and not allowed to climb trees, shrubbery and other landscape features, like vines naturally want to do.
Pink, red or white are the only choices. There happens to be a darker shade of red. Yellow throats are more conspicuous in white flowers. Otherwise, there is not much variation of color amongst the various mandevillas. The flowers are very similar in both color and form to those of related oleander, but are larger. Some are as wide as three inches. Small flowers can have pointed petals.
Even within its native range, blue dawn flower, Ipomoea indica, can be a problem. There are not many other plants in some coastal regions of Peru that can avoid getting overwhelmed by the aggressive wiry vines. These vines grow roots where they touch soil, so can spread indefinitely over the ground. Vines that succumb to frost over winter regenerate as if nothing ever happened.
Like Ginger and MaryAnn, choosing between the flashier hybrids of clematis and the anemone clematis, Clematis montana, might not be so easy. The fancier hybrids have the bigger, bolder and richly colored flowers that the genus is known for. Anemone clematis has smaller and more subdued flowers in soft pastel hues, but is more prolific, more vigorous, and blooms for nearly a month.
There are so many different specie involved with the extensive breeding of the modern cultivars of clematis that they are not even assigned full Latin names. They are simply known as ‘clematis’ (without a specie name), with a respective cultivar name. Clematis X jackmanii is the oldest known hybrid, so the name is often applied to other hybrids, whether or not they are actually related.
Lawns composed of turf grasses are the most functional, but also the most demanding forms of groundcover. That is old news. There are so many other less demanding low growing plants that that can cover the ground in areas that are not used like lawns are. Sometimes they work nicely just to control weeds. Sometimes they help to control erosion on otherwise unlandscaped hillsides.
The popular wisterias that bloom so profusely before their new foliage appears in spring are Chinese wisteria, Wisteria sinensis. Others specie are rare. The impressively longer floral trusses of Japanese wisteria are not as abundant, and bloom late amongst developing foliage. American and Kentucky wisteria are more docile small vines, but their floral trusses are both short and late.
Foliar tapestries are impressive in the right situation. 

This is one of those plants that many of us have strong feelings about. Many of us who remember it from when it was more popular in the 1970s might consider Algerian ivy, Hedera canariensis, to be an aggressively invasive weed. Those of us who are less familiar with it might appreciate it as a vigorous and resilient groundcover that gets dense enough to exclude most other weeds.