I'm not sure I entirely understand what you are looking for. Will the area you are planting be mowed? How much foot traffic?

Some of the low groundcovers I have that have spread into my grass lawn include Ajuga, Fragaria chiloensis, and Potentilla neumanniana.

REdneckgrower:
Sorry if it wasn't clear. The plan would be to have an area that didn't need mowing so that the furniture could remain in its place. Not a lot of foot traffic. The groundcover would need to be hardy enough so that the grass would not encroach (and therefore the area would need to be mowed). I don't mind pulling the grass as the new groundcover got established but once established relatively free of maintenance. Nancy

OK, got it. I also should have asked about exposure; sun? shade? part sun/shade?

Anyway, I already mentioned a couple I like. I have a large space with a combination of Fragaria chiloensis and Potentilla neumanniana. There is a nice contrast between the foliage of these two, and there are yellow flowers on one, white on the other. Once established, it completely carpets the ground. I have it interplanted with some Sedum. Looks real nice.

If you're looking for a more 'grass-like' look, but don't want to mow, you might consider Ophiopogon, Mondo Grass. But, it will need some shade, and takes a while to establish a dense groundcover.

Vinca minor is nice. I also like variegated, small-leaved Hedera (ivy). I use some Sedum in smaller places.

For taller groundcovers, I use Euonymus fortunei 'Colorata', or Campanula takesimana (be careful of this one, and some other Campanulae, as they may/will invade your lawn!), or Sasa veitchii (a small bamboo; will also spread into your lawn, so you'll have to curb it, mow it out of the lawn, or periodically cut the rhizomes with a shovel; real pretty, though).

I'm sure others will pipe in with their favorites. Cheers!

Ooops, I said I didn't ask about sun exposure, but it's in the title of your post! You said SUN LOVING..., and I failed to notice that; sorry. So that will limit some of the above choices.

Thanks. I love both the fragaria and the potentilla (especaially the potentilla). ANd they both seem to like sun. Do you order them from a catalog
N

Yes, they both like sun. And, they are relatively drought tolerant once established. I'm sure you can find them online, but I'm not sure where. They are easy to propagate, so they should be all over the place.

I originally bought mine years ago at Home Depot in a 6-cell pack, though I've not seen them around since. I'm sure your local nursery could order them for you, if all else fails.