The first plant that comes to my mind is shrimp plant. There are several varieties.

I second shrimp plant. They bloom for months on end, are disease-free and are easily rooted and available through swaps. Another really nice plant that will do well there is turks cap, especially the pink one "Pam Puryear" and this plant also blooms for months and months. Another healthy plant that I enjoy is David Verity Cuphea, although I am not sure if it will bloom as much in shadier gardens. This is also readily available. Another is justicia spicigera which has really nice orange blooms through most of the year...also readily available.
Molly

thanks guys, i'll have to look up these plants, the only one I know is shrimp plant..i'll go lookin now ...again, thanks molly

I really like turk's cap for shade - it blooms well there and I think the plant's form is better in shade than in sun.

Another non-stop shade bloomer is "Lady in Red" salvia - there is also a pink form. So whether you have pink turk's cap or red turk's cap, you'll have a coordinating salvia.

Lin

Pigeonberry is another option, but it might want a little more light. I have two planted where they'll get some sun during part of the year, at least a couple of hours' worth, but the rest of the time they're shaded by oaks and pecans. I have a Turk's Cap in a similar placement, it gets morning sun but is planted underneath the oak tree's branches. The Turk's Cap dies back to the roots (or almost, depending upon how cold it gets) while the Pigeonberry just goes dormant. Where you are, the Lady in Red salvia will most likely be an annual, but it reseeds freely. That said, I have a number (in full sun) that are coming back from the roots this spring.

Iris would be another option, although they only bloom once. Dward Katie Ruellia would also work. I don't know how often you can get pass alongs (I can share a couple if you're close enough) but they're inexpensive in the stores and will spread on their own. I have them planted in mostly shade and they're not invasive at all. They die back to the roots during the winter but pop back up come spring.

Another option would be cast iron plant, it's "just" green leaves, but they'd be good to mix in for a different texture. I have some in a corner of the yard that are doing just fine on benign neglect. Asparagus fern might be another option, it's supposed to be OK down into the teens, but I only have it in pots that spend the winter in the greenhouse.

Another option to consider: if you have any tropical potted plants, that's a good area for them to live except during winter. I keep my mother's potted plants underneath the oak tree where they might get a bit of dappled early sun but that's it. The only drawback is that you need somewhere to keep them over winter.

That's all based upon my experience: my backyard has a mature pecan and two mature red oaks, with two small live oaks on the fence. There's not a lot of sunny areas back there. :) Oh, the red tip photinia hedges on two sides and neighbor's mature trees on the others don't help, either.