This is a question close to my heart.
Over time, I tried a few different solutions for this. My answer is it really depends how many scarfs you have and how often do you wear scarves.
I used a flat scarf hanger similar to what Angie suggested. It worked great until I needed more than a few of them. (Scarves are sentimental items for me as most of mine are inherited or gifts so I tend to accumulate them.) Along with my costume jewelry and belts also hanging next to it, the accessories took half a rack in my walk in closet.
Once this solution was too bulky, I tried my husbands extra tie hanger for a while. Since it holds more and is less bulky in space, it worked to save space. But I wear scarves often and messing with the wires of the tie hanger evening and morning made me seek for a new solution.
Then I used sock organizers that I normally use for my socks and underwear. (http://www.containerstore.com/.....d=10000146) This worked great for silk scarves. You can roll the scarf so there is no line when you unroll it before wearing.
For pashminas and thicker scarves, I simply fold them and pile them in a clear cube drawers so I can see the colors top to bottom.
Sorry for the long post!