The choice of groundcover depends on whether you want something that you can walk on. For areas that don't get any foot traffic, I love Ajuga reptans, which forms a spreading carpet of low-growing plants with rounded leaves. The spring flower spikes are blue and beautiful.
Ajuga spreads quickly by way of runners, so you get good coverage in a short time. Young plants should be spaced about one foot apart and watered regularly until they get established (usually one month to six weeks). After that, you can ignore the ajuga. It will do all the work!