"Stylists and decorators know that rugs are as effective off the floor as they are on. Used as wall hangings in catalogs and photo shoots, they are a secret weapon in the mission to create full, interesting, and beautiful rooms." - Apartment Therapy
We gathered several examples to inspire you.
For lighter rugs, like kilims and flat weaves, you could use clip rings. HOWEVER, be sure to periodically rotate the rug so it doesn't stretch out of shape from the weight of the rug. And use double the abount of rings than you think you need. This will disperse the weight,
Velcro is a good hanging option too. "a strip of Velcro is hand-sewn to the top back of the textile or rug. The soft, fuzzy Velcro part goes on the weaving; then the stiffer, matching Velcro strip is stapled or glued to a wooden board. The wood is then mounted on the wall wherever studs are located. The textile is simply pressed into place. Some individuals prefer to machine stitch Velcro first to a buckram or hair-canvas strip, then hand-stitch that canvas to the rug. If the textile is soft and flexible, this stiffens and supports it a bit. I occasionally secure a slit-tapestry kilim by stitching at staggered intervals straight through the center of the Velcro, as well as along its edges." - Marla Mallett