Hi,
I planted vinca vine under my Maple tree 3 years ago. Now all the roots are covered and I don't have to mow the scraggly grass anymore. I like the violet colored flowers and it really filled in nicely. Hope this helps.
Jane

Another option would be Lamium. There are several cultivars with pink, white and creamy yellow flowers -- all would look nice with vinca and avoid the monoculture look. I would avoid English Ivy -- it would definitely grow up the tree, but tends to take over. Sweet autumn clematis might work on the trunk, very vigorous and low maintenance, with scented white flowers in fall. I've also had success with Clematis tangutica as both a climber and ground cover. It has cool little yellow bells in summer that later burst into fuzzy Dr. Seuss seed heads that last all winter.

http://faq.gardenweb.com/faq/lists/shade/2002083540029272.html

This link is under the FAQ section.

Here is what is growing very happily under the huge silver maple in my back yard, which is dry, dappled shade:

Trilliums (many varieties, grandiflorum, erectum, prairie, nodding, etc.)
Virginia Waterleaf
Meadow Rue
Zig Zag (or Elm Leaf!) Goldenrod
Fire Pinks
Jack in the Pulpit
Hepatica
Soloman's Seal
Jacob's Ladder
Native Columbine(Aquilegia Canadensis)
Bloodroot
Dutchman's Breeches
May Apples
Fox-glove Beardtongue
Bleeding Hearts
Twin-Leaf
Virginia Blue-bells
Black Cohosh
Goat's beard
Wood Poppies
Tiarellas Cordifolium & Wherriyii
Bottlebrush Grass
Lady Fern
Christmas Fern
Ostrich Fern
Maidenhair Fern
Green Dragon
Pink Turtle's Head (Chelone Something or other)

These are all native plants, because that's what I'm into. But, they are used to, and have evolved for growing under maple trees, or other hardwoods. I do supplemental watering every 2 or 3 weeks if we are droughty in the summer. And that's it. No muss, no fuss. It might be nice to fill in with hostas, as most of these natives are ephemerals that die back after blooming in the spring. April

I also had some grass and lots of roots under a maple that is out by the roadside. I finally saved all the leaves in the fall and tossed them under the tree out to the drip line. The next year all had mulched down and I planted in some cinnamon fern, hostas, columbine, New England Asters, Sweet Annie and Sweet (a guys name) Something-else-that-I-forgot and several mint varieties. The mint is welcome as it filled in and under that tree and was just beautiful. Now the other plants have grown well and if the mint tries to get out of hand I only spend a few minutes once a year and yank it out at random and everything seems to be happy. If I were you I would just pop in a bit of this and some of that just to see how well things do - anything is better than the scraggly grass that is for sure! The one thing I like about the mint is that it smells sooooo good when the cats wander under the tree or the soccer balls from the grandkids roll over it! There is nothing that can hurt it and it always makes a good showing! I notice that when the neighbors walk past they put out their hands and let them pass thru the mint just so that they can smell the frangrance that wafts up! I almost forgot to say that every fall we rake up the leaves, run the mulcher mower over them and toss them under the tree and after 8 years of doing this the soil under there looks great even tho the roots come to the surface. Whatever you do you can't go wrong! Happy gardening!
Cheers - Kiwi

There are a few ways to get rid of the grass, Roundup being one of them. Please use carefully and cautiously!
Next, find a cheap source of wood chips and spread them over the dead grass. (Don't bother to dig or remove the dead grass). If you plan ahead, and arent in a hurry, use newspaper topped with mulch and let that sit for one season.
During the next year, put grass clips, chopped leaves and even another thin layer of chips over the old lawn.
You might have to put in pots of annuals to have color on the lawn during this transition period.
After a full year, you should have NO grass, and a somewhat healthy layer to plant in.
Then, hey, go for all the suggestions above. Happy gardening!
Pondy

A bed under a tree will do much better if raised slightly, not enough to smother the tree roots - about 6" or so. You'll also need to fertilize and water more often, as the tree roots will take all the nutrients and moisture from the soil.

I think, Sheryl, the maple tree's roots would grow into that new soil very quickly and you would have the same problem in another year. I think, also, 'smothering' a tree's roots with excess soil is a sure-fire way to distress the tree, putting it at risk for death and disease.

No maintenance perennials I grow under a similarl-sized Norway maple, also in a tiny front yard, include big-leaved aster and woodland sunflower. In sunny parts, low-growing sedums do well.

Bogart,
What do you call"No maintenance perennials" ????

You plant them, you watch them grow, you enjoy the flowers in July/August/September, you cut them back in the late autumn or early spring if you don't like the stalks sticking up and the snow hasn't flattened them. They'll spread via underground shoots (slowly) or by self-seeding(more quickly if you let them). Occasional watering, especially for the sunflowers, in very dry periods.

Actually, (insert sheepish grin,) I intended to say 'low-maintenance.'

Please don't use English Ivy or Sweet autumn clematis, they are considered invasive.