I have an area next to my house approximately 6' by 20' that gets almost no sun. I want to plant a ground cover garden, in other words I want a variety of plants that will serve as ground cover as well as provide color and interest to the area. What kind of low 6" to 24" plants can do that?

If you don't mind having one of the most invassive plants in the world, try houttynia. A much more behaved groundcover is 'Big Blue' liriope.