Hostas are a topnotch groundcover for shady areas. Plant them on a tough-to-mow hillside to create a lovely, carefree garden bed. If you have a steep slope that water runs down so quickly the soil can't absorb moisture, try breaking up the hill with rock
Epimedium Red Barrenwort -Berberidaceae can tolerate dry shade such as the base of a tree(once established). Red spring flowers, heart shaped leaves, and bronze fall foliage make this a multi-functional plant.
Golden Japanese Forest Grass - I really cannot get over Japanese Forest Grass (Hakonechloa macra 'Aureola', zones 5 to My favorite is the variegated variety. I planted mine under a Japanese maple, and the contrast was genius and it has so much movement.