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.

white vinca minor. http://farm3.static.flickr.com/2577/4144665169_0acdf816bb.jpg it's fairly invasive, but easy to remove (shallow rooted)

Planting recommendations may say otherwise, but I've had great success with pachysandra (japanese spurge) in both full sun (south facing wall) and full shade. Very hardy and excellent groundcover, attractive, and evergreen for me. Read my response to "ideas for shade groundcover as lawn replacement" - a thread posted just after your own on this forum. I don't have deer but I believe they are deer resistant.

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.)