Bishops weed, also known as snow on the mountain is a super hardy varigated ground cover. It's delicate bright green foliage with a white trim makes it a unique feature in a garden. They are great spreaders and cover unsightly areas in landscaping or where you can not keep mowed and maintained well. They hide ground debris and weeds.
Home gardeners who like small foliage that is well-behaved should consider English ivy. This vine is perfect for hanging baskets, containers or as a ground cover. English ivy is also a good choice for climbing on trellis, porches and other structures.
Garden phlox is a wonderful lavender ground cover that turns a pinkish color in low alkalinity soils in late summer. It's versatile and makes a carpet like appearance full of delicate blooms covering the entire plant. Perfect for planting on hills or near rocks to gently climb and bloom all summer long.
Trumpet Vines is another great hardy one that can be trained to climb primarily because they tend to grow towards the sun. When training your vines to climb fences or a trellis, interweave the new shoots through the openings as they grow. If you are training vines to twine around masonry or trees, you can attach a wire to the structure at the base for the vine to climb. Taking just a little time to train your vines will bring big rewards. Your fence or other structures will have good coverage as these plants grow upwards.