The Mexican Tradescantia species are good groundcover plants. They are sophisticated cousins of the weed which plagues most Sydney gardens, Tradescantia fluminensis - better known as wandering trad - but they are generally not quite as invasive like that horrible one. Tradescantia zebrina (ht 20 cm) is striped in silver and green and has purple undersides, and is more keen than some of the other coloured cultivars to take over your garden than the others, so I confine it to dry shady spots where little else will grow, as it needs minimal water.
Tradescantia zebrina provides an excellent foliage contrast to other plants, including its cousin Tradescantia pallida 'Purpurea'. It can be effective wandering through clumps of bromeliads (especially those with silvery leaves or purple tinges to their foliage) to fill in any gaps.It makes a good subject for a hanging basket if you are too frightened to let it loose in your garden.
I also think it can be useful to cover blank areas where spring-flowering bulbs are dormant over summer. Just remember to pull it back once the bulb foliage starts to reappear in autumn. When it 'wanders' too far, pull up all the bits you don't want, leaving just a small piece: like its scary cousin, it will quickly regrow! It can get a bit straggly after a while so trim back in early spring or simply pull it all out and replant some bits. There is a darker-leaved variety (pictured above) that can be useful in the garden as a contrast.
All forms of trad can escape into bushland, so be very cautious in growing it, or keep it in a pot.