Here are a few that will work well

ACORUS gramineus (Sweet Flag)
AJUGA (Carpet Bugleweed)
CERATOSTIGMA (Dwarf Plumbago)
EUONYMUS fortunei (Wintercreeper)
GELSEMIUM sempervirens (Carolina Jessamine)
HEMEROCALLIS (Daylily)
HYPERICUM calycinum (St. JohnÂs Wort)
JUNIPERUS (Juniper)
LIRIOPE spicata (Creeping Lily Turf)
MAZUS reptans
PHLOX (Creeping Phlox)
RUDBECKIA fulgida (Black Eyed Susan)
SCABIOSA (Pincushion Flower)
VINCA major (Large Leaf Periwinkle)

I know some don't think of some of
these as groundcovers but they work
well as groundcovers spreading quickly.

Drought tolerant and perennial? If you have good drainage several of the short sedums are fast growing and like sun. Sedum tetractinum/paddle leaf is my current fav (grows really thick) but a lot of the sedums are fast growers. Ice plants, thyme, and I have some kind of stoloniferous phlox that is spreading nicely. Some of the dianthus would work. I have some coreopsis that stays under a foot and is getting bigger around every year. Another I love on a sunny bank is the purple homestead verbena.

ice plant, delosporum. A succulent ground hugger with pretty flowers. Break off a piece, stick it in the ground and it will grow. And as mentioned above, there are lots of sedums which you can propigate in the same manner.

Homestead Purple verbena is a good one. My MIL has a white lantana that is hardy and aggressive.

Will it get much foot traffic, or not so much? My new favorite plant can be sewn from seed, and comes in silver or green. It is Dichondra argentea, and the silver one is 'Silver Falls,' but the green one is also pretty. Not something that you'd walk on, but gorgeous, and would work if you had a stone path or something.

Here is a site. I think it's the detail page that tells you just how fast each spreads.

http://www.jeeperscreepers.info/listall.html

Here is a link that might be useful: Jeepers Creeper's page

Laurabs, I am curious if this plant has been perennial for you in 7b. I've used it quite a bit cascading out of pots. I've found information that it is only hardy to zone 9 and the tag information says hardy to 30 degrees or zone 10. I did find one site that said hardy to zone 8. I had it planted in the ground last year but it did not come back for me. I'm in zone 8. Adele

I just got it this year and it had no tag, so I just read up on it. You are right, it is supposedly not hardy here in zone 7b, so I was thankful to read you could also grow it by seed. This one plant I have I may pot up and bring in because I like it so much. I'd be putting it in with coleus and impatiens that I can't bear losing either.

Why or why are some of my favorites not hardy in my zone??

I agree about the ice plant or creeping thyme. Dianthus cottage pinks will work, but bunnies or fawns pulled mine up out of the ground this past winter after leaving it along the previous winter.

Phlox subulata is evergreen for me and I've not had a problem with anything eating the foliage. Iberis (candytuft) is possible. Oregano is also a possibility.

Rosemary (carpet type) smells great with tiny blue flowers. It can get 1-2 ft tall and 8 ft wide very quickly. I have two clumps and love it. It is especially beautiful where it can drape down over rocks or walls.

Cotoneaster is available in a number of types for groundcover. Some of it can look really unkempt, but I have a variety that is fairly flat and beautiful year round. My landscaper installed it at our waterfall, so I don't know the exact variety. However, it also exceeds your height preference.

I have hypericum calycinum along our guest parking area(full sun)and it spreads quickly 18"high x 3ft wide.

I don't have personal experience with creeping raspberry, but I've read a few good reports on it in FG mag.

I would use lavender if not for your height limitation. Anyone with bee allergies shouldn't plant it.

Best to purchase in flats to save money.

Now if you ever want a part shade groundcover, creeping jenny can't be beat. If it's planted underneath shrubs where it can hide some from all day sun, it works. I have it everywhere.

Cameron

I have creeping raspberry that Cameron mentioned and depending on what you want it for it's a nice groundcover. It has a kind of coarse wiry texture, but it's one tough plant and spreads well and stays low without taking over the world.
Dana

laura, regular green dichondra is hardy here- and last i looked, park's sold seed. people in california use it as a lawn substitute. i have a good bit volunteer in my yard & beds, and just leave it. it is hardy, but does lose some of the foliage in winter. and it can't be stepped on much. i tried transplanting to paths and it died out quickly. blue star creeper would work nicely, too, though i think it's happier with a bit of shade.

i think creeping jenny can take a good deal of sun as long as it has moisture. so it's great for ditches and that sort of thing. that's where i grow mine. it can take being submerged and reasonable dry spells both. also, you could consider some mints in your sun so long as they had some moisture. problem might be that they take over! if it's a dry area, what about creeping lemon thyme or lime or caraway? many of the thymes stay low and a varied patch would look great.

i can't believe i'm mentioning this because it's quite invasive- but it is great for groundcover in dry full sun. if you have an area it can't cross it would work wonderfully. it's oenethera- aka cape primrose or sundrops. comes in pink, white, and i think yellow. you want one of the types that stay low and bloom all summer in 4 petalled california poppy like flowers- some get tall and are biennual. don't even consider planting it if you don't have a barrier or you'll regret it. it comes back from every tiny rootlet left. i just dug the last (hopefully) of mine out of a bed and plan to have it in a trough or low pot. i love their look, just not the rambunctiousness.

Thanks for all that. I love green dichondra. I already have some of the creeping jenny - hubby doesn't like it though, and it seems to attract snails? Not that I can see any damage. Maybe it's just the low position it's in; it definitely handles driveway runnoff or long drought wonderfully. But I will look further into the green dichondra. Especially in the back yard - I'd love that.

I've been studying all sorts of groundcovers. A neighbor who has never had any success with grass just had a bunch of landscaping put in with some nice stacked stone walls. I so want to go over there and start planting stuff in all that open ground she has, especially flowering thymes to cascade down her walls. Hold me back!