I guess I forgot to add that this area is in front of our shed so whatever we grow needs to stay low to the ground. Preferably 2-4" or so. Also this is a rather large area. Approx 10-15' wide by 25-30' long I'm guessing. I haven't been able to actually measure it yet becuase of all the rain lately.

Vinca would be a good choice, but I'm not sure if it could stand in water and survive long. Creeping Jenny is a beautiful shade groundcover that loves moisture, it's bright colored and tough. Lily of the Valley is another one to consider, and also Lamium, although if it's to hot it wont look nice in summer. Good luck!

Jen

symphytum grandiflorum, Comfrey, miaght be worthwhile looking in to.

Classic pachysandra will tolerate any of the given by you conditions except it doesn't like to be stepped on.
Even a very light traffic.
Vinca minor could withstand ocassional step on, but also is not suitable for traffic areas.
Moss?

The requirements you've outlined are pretty daunting. Few plants will tolerate submersion in water for any length of time, full shade eliminates many possbilities, and withstanding foot traffic complicates matters even more. So..
How about a stone or masonry path to deal with the foot traffic issue?
What grows there now? This could be a helpful indication.
Creeping jenny might work and so might sweet woodruff, but you would need a huge number of plants to fill an area this size.
Moss would be a good choice if you can find a source of sods. Perhaps there's somewhere they could be collected with the land owner's permission. Moss is a terific germination bed for weeds of all types, it's hard to rake leaves up without causing damage, so it's not a low maintanence solution.
If nothing at all grows here now indicating near impossible conditions for plants, I think I'd opt for a stone/masonry path surrounded by gravel mulch (bark would float away). You could certainly plant ferns and other shade tolerant plants here and there. Any shade tolerant plants which grow in flood plains should be suitable.

I think mainegrower has a really good idea. I'd probably use pine straw for the ground cover. It doesn't float away easily, and it looks really nice with the occasional plant peaking up out of it. Plants that I have in moist shade include Solomon's seal, ligularia, astilbe, and chelone lyonii. All of them can take standing in water for short periods of time. I don't know of any groundcover.