Vancouveria hexandra comes to mind, it's native and very invasive.

Campsis radicans (trumpet creeper) and Parthenocissus quinquefolia (Virginia creeper) are native, invasive, and can be grown in shade or part shade.

Anemone canadensis or Meadow Anemone becomes rampant and can be considered a ground cover. In my yard it loves deep shade to part shade. Very easy to grow.

I would not call Vancouveria a native - it's native to the West Coast.

Milo, can it tolerate drought?

Sanguinaria canadensis, Jeffersonia diphylla, Actea pachypoda, A. rubrum, Caulophyllum thalictroides, Dicentra eximina, Cimicifuga racemosa, Trillium grandiflorum, Podophyllum pedatum, Stylophorum diphyllum, Uvularia grandiflora to name a few.

I would call Vancouveria a native..it's native to North America.

I can't grow Northern Sea Oats to save my life. I was told to grow it it full sun, so that's what I did. It never came back.

I was going to recomend Anemone canadensis as well. It's very pretty and it is fairly invasive. I love it though because it is so pretty and it seems to be able to take a beating. I'm growing some out in the back alley and I do litterally nothing to it and each year it takes over a little more area where the quack grass would like to be. I would say it is of simmillar invasiveness as lilly of the valley.

Vancouveria is a cool plant but not nearly as nice as many of its close relatives, epimediums. And although Joshua trees are native to North America, I wouldn't think they would be appropriate for many local conditions and are far less "native" to eastern woodlands for example than epimediums and other species that are closely related to one another, but only separated because of geological and geographical events. :-)

One of the best for shade not mentioned here is Asarum canadense. It spreads really well. Also some Hydrophyllum species spread like crazy, as well as the under-utilized Pachysandra procumbens.

Columbine(aquilegia canadensis)seeds itself around like mad. Virginia waterleaf does, too. Soloman's Seal(polygonatum biflorum?) and Bloodroot are also spreaders, once established. Zig-Zag goldenrod(Solidago Flexicaulis) is also aggressive.

Jewelweed is a great fast growing annual that can outgrow most troblesome annual weeds.I make sure that any open soil on my property is covered with its seedling in the spring.It will grow praticlly anywhere except where its too sunny and dry.Great deer fodder too.You got to pull up all the mugwort though.

Hardy ageratum (eupatorium coelestinum). It has a fluffy blue flower late summer to early fall. It can take over a bed if you're not careful. But I have a fondness for blue so I just pull out the unwanted ones.