If the area is very shady and not too large, you could just mulch it. However, if it's too big for that solution the next question is - what's the area used for? If you are going to walk on it then you're limited in your choices.

If it's just a decorative area consider Ficus repens or Creeping Fig. Works well in the shade, handles drought and cold quite well.

Not a decorative area. Just a couple of relatively small areas in the corners of my yard. No foot traffic, but dog traffic. Can't use mulch. Just anything that will grow fast and spread.

I have creeping fig and it's very nice but a VERY slow grower.

naplesgardener - If your creeping fig is growing slowly it must have something to do with either the soil or some form of contamination. I've not seen many plants grow as fast as Ficus repens. I covered a wall 4' high and 8' long in less than a year from a single plant in a 1 gallon can.

wandering jew or ferns.

Thank you all. I will look into those.

Dwarf confederate jasmine!

Here is a link that might be useful: Asiatic jasmine