I cut strip of various from old clothing that was destined for the rag bin, scraps left from other crafting projects, and other lengths of ribbon, lace, yarn to braid into it's self in a circle randomly or to create patterns. Pretty much anything works and i like the mixing of textures and textiles using fleece, t-shirt material (I've collected cut off sleeves from co-workers and brothers), cotton, and even terry cloth from old towels. I found it easiest for me to keep the cut strips in plastic bags, seperated by color for ease.
Over the summer I kept one by my bed and moved it to in front of my door to help the tracked in dust from going any further. They are sturdy enough to shake out or thrown in the washer and dryer. (I've already washed mine.)
Check out more on my blog: http://craftrebel.blogspot.com/2011/03/braided-rag-rugs.html