Fat quarters are what brought me to this site. I was surfing and looking for what to do with them because my SIL had given me a package saying there should be enough to make quilt. I don't particularly like the fabrics but want to sew something (simple) so I can let her know that her gift was appreciated. Like you, I had no idea what to do with these chunks of fabric but through this site I learned that there are actually whole quilt patterns for them. Books full of 'em!
My FQs shrank when I pre-washed them so only one of the 20 was still 18x22. The rest ranged from there to about 15x19. Not one yielded the number of strips called for in the pattern.
The pattern is called "Wickedly Easy Quilts" and I found it through a link on this site at
http://www.byannie.com
After all this FQ research, I'm excited to start making quilts using them.