While they won't tolerate as much foot traffic as a lawn, a few low-growing ground covers can take some traffic.
Chamomile (Chamaemelum nobile, Zones 1-24, 30-43) forms a soft-textured evergreen mat of aromatic leaves in bright, light green. Stems root as they spread, forming a solid cover. Small yellow flowers appear in summer. Space 1 foot apart.
Lippia (Phyla nodiflora, Zones 8-29) creeps and spreads toform a sturdy mat of 3/4-inch, gray-green leaves. Tiny lilac to rose flowers bloom from spring to fall; these attract bees and can be mowed off, if desired. Dormant in winter. Space 1 to 2 feet apart.
Scotch moss (Sagina subulata) and the very similar Irish moss (Arenaria verna) both grow in Zones 1-11, 14-24, 32-43. Good choices for planting between stepping-stones or to cover a small area, they form dense, compact, mosslike masses of slender leaves on slender stems. They grow best in good, well-drained soil. Space 6 inches apart.