I've put an orange chevron rug in my son's nursery and a pink shag rug my daughter's room. The center of the room is usually the play area and the rug helps prevent premature wear of that portion of carpet. They also bring an extra pop of color.
I also put a black and white graphic rug in the office. You can see a peek of it here.
Here are some other examples of rugs on carpet.
This large blue chevron rug makes a bold statement in this room. It ties in the blue and brings in another pattern.
The floral rug in this child bedroom anchors the bed and brings in more pastel colors from around the room.
This rug defines a seating area. It draws the eye in to this space and separates it from the rest of the room.
Do you have rugs layered over carpet in your home?