Creeping Sedum is fast-spreading, drought tolerant and easy to keep in check. It grows in the hot, full sun or in the shade. It doesn't seem to have any special soil requirements. In June, it's covered with tiny yellow flowers.
Creeping Thyme 'purple rain' | Vigorous and Hardy ground cover | Sweet scented flowers | Stunning colour | Grows in most regions of Australia | Full Sun to part shade | Available as seeds from The Climbing Fig Online Garden Store
Dragon's blood sedum may be the hardiest and most versatile of all weed-suppressing ground covers. A cultivar of the succulent Sedum spurium, Dragon's blood ('Schorbuser Blut') is hardy in Zones 3-8. Not only does it grow in full sun as well as partial shade, but it also thrives in poor soil.