Here's one. Cut strips of fabric. Layer backing fabric and batting (I would heavily starch the backing fabric first). Draw a straight line down the center of the quilt (or snap a chalk line). Line up two strips of fabric right sides together with raw edges along the line. Sew a 1/4" inch seam on that side. Open up (and maybe iron) so that both strips are right sides up. Add another strip and sew that down, flip right side up, add another strip, etc. This has no matching seams, and the quilting is done at the same time as the sewing.
A jelly roll quilt would also be an easy one with no matching seams. I just saw one at the quilt guild that was *fabulous*, made from leftovers of tractor and boy fabrics on the right side. What was unusual was that the quilter sewed *all* of the jelly roll seams before ironing any of them! Turned out great!
Here's a jelly roll quilt variation that includes a border and still doesn't have any matching seams:
http://www.etsy.com/listing/89000268...-easyone-jelly
Edit: I just want to add that it makes a big difference if (1) the quilt has no seams, or (2) the quilt has no matching of seams!