Moss sedum. I have it growing in full sun and shade. It's completely winter hardy and withstands the hot humid summers with absolutely no care. It roots readily and spreads quickly. It is covered with small star shaped blooms in late spring/early summer and remains a lime green year around.

Here is a link that might be useful: Link for info on moss sedum

I have full sun and no real trees. I grow lantana (there are variegated varieties), creeping buttercup (ranunculus) variegated mint, sweet potato vines(freeze back in the winter), creeping jenny. I also have several evergreen daylilies mixed in in clumps.

Dwarf oreganos. Beautiful, and come in a wide variety of colors and is especially nice with various sedums growing through it.
Another idea is hardy iceplant (I don't know it's zone preferance) it can take humidity in stride, and is a flowering machine. Evergreen.

Are you wanting really low growing plants? I can think of some taller plants that love full sun.

Caryopteris: Bluemist or Bluebeard-various cultivars some with yellow and variegated foliage, heights and colors

Dwarf Spireas: I have one called 'Golden Elf' that is very small and is very handsome with yellow foliage

Viburnum 'Conoy': a comparatively small hybrid-gets about 4-5' by same, has gorgeous shiny evergreen foliage with lightly fragrant white flowers and nice red maturing to black berries

Deutzia 'Nikko': small growing(I have one that is about 5 years old and it is about a foot tall and two foot wide) deciduous shrub with purplish fall color and frothy white flowers in spring

Trachelospermum asiaticum: Asian Jasmine- extremely tough vining evergreen that gets about a foot tall, after a couple years will have small white flowers

Dwarf Rosemary: I have one called 'Blue Boy' that has been fabulous! I planted it in 98 and as of now it is 1'4" by about 2'5". It seems like this plant blooms for 10 months! It is always blooming!

Keep looking and researching there are literally thousands of possibilities. Good luck.

rocks,
If you don't mind a plant that takes over, I recommend ajuga. I have mine in full sun and it does very well in our brutal dry summers. It also stays evergreen for us folks in warmer climes, plus it has beautiful late spring blooms.

You can find many nice groundcovers at steppables.com.

I recommend:
-Ajuga "chocolate chip"- it doesn't melt out and die like other Ajugas- probably more resistant to fungi. Blue flowers in spring are beautiful.

-Sedum requieni. Like most sedums it is easy to propagate, is evergreen, hugs the ground and tolerates drought in full sun.

-Lysmachia nummularia "Aurea"(golden creeping jenny): rather invasive but beautiful.

-St. John's wort-it is evergreen for me and tough as nails. Pretty yellow flowers in summer.

Susan

Investigate Ophiopogon. It comes in a standard size (4-6") and a dwarf (1-2"). It takes full sun or full shade and is evergreen, not agressive, drought tolerant, and virtually carefree. The dwarf variety is particularly attractive.

I second the Ajuga suggestion. I have Chocolate Chip and Caitlin's Giant planted in an area that gets bright shade with no direct sun, and in another area that receives the full effect of our HOT Southern sun in the Summer. It does just great in both spots.
Pennyroyal is another good spreader and it smells nice when you step on it. Gotta watch it though as it can get out of hand and spread quickly to places you don't want it to go. My brother planted a tiny bit outside his backdoor and the next thing ya know it had claimed a sizable chunk of his backyard. But you can mow over the stuff just like grass. (ie., it takes heavy foot traffic and abuse just fine.)

I live in South Central Florida, about 60 miles south of Ft. Myers, the sun is real hot here. Will any of these suggested plants do well for me?
Thanks,
Lorraine

I am also looking for some kind of low-growing, easy maintenance groundcover. I'm having a hard time finding something. I've thought about Ajugas, but am concerned that they may spread into my St. Augustine yard. Any experience out there on this issue?

Also, what about low-growing chrysanthemums?

Helianthus debilis~
A wonderful full sun GC.
(Let me know if you are interested in some cuttings~)

Here is a link that might be useful: Beach Sunflower

Seems to me most of the stuff being recommended is over 1 foot in height. I know that I, and I think the original poster, is looking for something less than 1 foot in height. There is a cultivar of Stokes Aster (Stokesia), can't remember the name of it off-hand but it is named on the Floridata description of Stokes Aster, which grows no higher than 10 inches. So far, this is my leading candidate. I'm also giving some consideration to a low-growning lantana (Trailing or Weeping Lantana), although this grows to 18 inches in height.

I use creeping thyme as a full-sun groundcover. It's virtually carefree and evergreen. I live in zone 8 in SC and have no problem with it. It covers thickly and crowds out weeds. It also has the benefit of being a culinary herb. We strip the leaves, use kitchen or craft scissors to cut them up (they're tiny!) and mix them into burgers along with a little Worcestershire sauce and minced garlic. Spectacular!

Ice plant, delosperma floribundum

Aptenia cordifolia (baby sun rose) has flowers in either light yellow or soft red flowers. It grows great in central Florida and it is said to grow well to zone 8. I don't know if you can buy seeds, but it is easily propogated from stem cuttings.

I want to plant something in a parkway that takes over and is little or no maintenance. I'm required to maintain the parkway but I don't want it and neither does the city. Thanks.