I've been pretty unsuccessful with a lot of the ground cover plants they sell at HD, although there was one that lasted a while in the summer but I don't remember its name. It looked slightly succulent sort of like purslane.

The only common weed I have in my yard now is the small spurge weed (and purslane) and I let it take over an area of my yard and I actually don't regret it (right now at least). It's almost like a carpet in that area of my yard and actually feels nice to walk on. It's the only 'ground cover' I've had that works with little to no watering. I don't know if I'd recommend doing that yet as I don't know if there's anything bad about letting it do this (maybe ants?).

As long as rabbits don't have access, Drosanthemum floribundum is a good one. It's tough, low, spreading, and has nice flowers in spring.

Rubus Pentalobus (Taiwan raspberry), mostly an ornamental groundcover but it does produce a few little yellow berries.

Here are some ground covers that would do well in a planter:

Lantana-I love the dallas red or the irene pink and the new variety-volcano which is yellow and red combined.

I love the trailing yellow gazania that I have in my planter box. It will fill up the entire planter. I selectively remove areas and add in annuals as I want to. Remember to get the trailing variety-it will flower off and on all year!

Happy planting! Deana Bella Fiore Landscape Design

I've had luck with pink blooming ice plant in Tucson, which has spread into a nice mat. It puts out pretty pink flowers in spring. I spray a little water on it weekly during June to keep it from going dormant; but even if it looks dead, it seems to come back with a change in the weather.