When I was sifting through my stash of crafting sweaters to find sleeves that would work for my jar cozy that I made yesterday, I set a pink sweater aside. Today, I snipped it into chunks that came together as a pillow cover.
I cut off the sweater directly beneath the v-neck, stitched a seam, and flipped it upside down which formed the lower portion of the pillow cover. The left side of the top is a sleeve and the right side of the top is the sweater's hood. You can see the hood's natural curve. I curved the corner of the other side to match it. I have quite an extensive collection of old fabric yo-yos... some I've made with vintage fabric and others that I purchased off eBay. I whittled down my yo-yo collection by one today by using it underneath a button.
Each sweater's style determines how the pieces might be used to form a pillow cover. If you run across a sweater with a variety of colors as well as textures, the possibilities increase. Martha Stewart's site has a photo that may provide inspiration, however it would have been more beneficial if it had included a tutorial. You may be able to find a site that walks you through the process. I decided to wing it and see what developed. I think the most important consideration is maintaining the authenticity of the original sweater so that you can see the sweater's details (e.g., ribbing, pockets, button closure) in the end-product.