Since I became interested in using more native plants, I have found several low-growing native ground covers that seem immune to deer. They have now been established for more than five years, so I have a pretty good idea what they will do—that is, if the rule sleep (first year), creep (second year), leap (third year)—is anything to go by.
Lyreleaf sage, Salvia lyrata, is available both as a straight species as well as a red-leaved cultivar, ‘Purple Knockout’. Besides the leaf color, the main difference is that the flowers are taller and bluer in the species than in the cultivar, and the species seems to spread more vigorously. I started with one plant by a path, which seeded so enthusiastically into both bed and path that I was able to move the seedlings into several places and establish colonies. This plant is said to prefer sun, but my experience is that it does fine in filtered sun/partial shade.
Pussytoes, or Antennaria, prefers sun. I acquired Antennaria plantaginifolia (plantain-leafed pussytoes) at the same time as Salvia lyrata, and although both spread, it seems to me that the pussytoes is more inclined to be happy in the sunny spots, although it seems to tick along nicely as a carpet under taller plants. The fuzzy flowers in spring are charming. This plant has spread nicely, but it is not so competitive that it can choke out aggressive competition (such as, for instance, the next example).
Anemone canadensis, or woodland anemone, prefers part sun but is basically up for anything. It’s an aggressive spreader, and it can be a thug. If you want a neat and tidy garden, it is probably not for you, since it does go everywhere and will clamber over very low growing things (like pussytoes). But if you have a confined space you want to fill in, or a woodsy or meadowy area where you want low-growing plants below the tall ones, this is a candidate.
One of my shady beds has a nice patch of Allegheny spurge, Pachysandra procumbens, a handsome, better-behaved alternative to the familiar, fast-growing Japanese type. It is semi-evergreen (the old leaves are quite battered by spring). This is a slow spreader, so it is a good idea to start with several plants if you hope to cover an area of any size. I began with one plant about 8 years ago, and after it seemed happy, I got a few more. But it is more of an accent rug than wall-to-wall carpeting. It has interesting flowers in spring, so put it where you can see them.
Another useful shade lover is barren strawberry, which (as another victim of the botany wars) has two Latin names: Waldsteinia fragarioides and Geum fragarioides. The crucial point is that both are fragarioides: strawberry-like in both leaves and flowers. They like partial to light shade, are semi-evergreen, and spread nicely. Having read that they would root in water, I rooted several cuttings one summer and potted them up. After I transplanted them outside about 10 days before leaving on vacation, I was pleasantly surprised on my return to find that despite a three-week drought, they seemed just fine. Several of them have persisted despite competition from other groundcovers (not to mention the weeds that I fail to keep on top of).
I suspect that everyone already has golden ragwort, Packera aurea (formerly Senecio aureus), but if not, you might consider it for large-scale ground cover. It spreads very effectively; it prefers moist, shady areas, but it is also fine with sun; it even copes with drought, although it looks rather sad. But it makes a fine yellow display in spring. Large perennials like amsonia and boneset are unfazed by it, but you might want to pull out ragwort seedlings crowding around the base of things that lack deep tough roots. If you decide you want it, you can just ask around: almost anyone who has it has plenty to spare.