Here's some ground covers that will grow in clay soil. This can be a difficult category to list, because other plants from other lists could be on it too. For example, dwarf yaupons are on the shrub list, but could also be used as ground covers. I will try to avoid listing too many duplicates.

In really heavy wet clay, these ferns will creep, spread and perform as ground covers:

Marsh fern (Thelypteris palustris)

Chain fern (Woodwardia areolata)

Virginia Chain Fern (Woodwardia virginica)

In wet, boggy clay where water can stand for days on end, these ground covers will thrive:

Grassy-leaved sweetflag (Acorus gramineus 'variegata')

Sedge (Carex spp.)

Horsetail (Equisetum hyemale)

Chameleon Plant (Houttuynia cordata 'chameleon')

Spotted Dead Nettle (Lamium maculatum)

Creeping Jenny (Lysimachia nummularia)

Inland Sea Oats ( (Chasmanthium latifolium)

Pampas Grass (Cortaeria selloana)

Mainden Grass (Miscanthus spp.)

In standard somewhat well-drained soil, these ground covers should do well:

Wintercreeper (Euonymus fortunei)

Virginia creeper (Parthenocissus quinquefolia)

Liriope/Money Grass (Liriope muscari, Liriope muscari)

Creeping Jenny (Lysimachia nummularia)

Asian Jasmine (Trachelospermum asiaticum)

Willowleaf Cotoneaster (Cotoneaster salicifolius 'repens')

Barberry Cotoneaster (Cotoneaster dammeri)

Quaking Grass (Briza media)

Sideoats Gramma Grass (Briza media)

Muhly Grass (Muhlenbergia spp.)

American Crossvine (Bibnonia capreolata)

English Ivy (Hedera helix) be careful, it likes to climb everything around it

Daylily (Hemerocallis hybrids)

Showy Evening Primrose (Oenothera speciosa)--is invasive in our yard even in heavy clay

Dwarf Junipers (Juniperus procumbens cultivars)

Creeping Junipers (Juniperus horizontalis cultivars)

Japanese Honeysuckle (Lonicera japonica) can be invasive

Common Periwinkle (Vinca minor) can be invasive

Greater Periwinkle (Vinca najor) can be invasive

More lists of flowers to follow.

Dawn