Sure, tons of pictures of scrappy quilts in all different colors and patterns of fabrics have been posted here. The queen of scrappy quilts is Bonnie Hunter of quiltville. Go to her website for lots of inspiration www.quiltville.com
You can make a scrappy log cabin with your 1" wide pieces and need to supplement them with some strips that are longer then 3 1/2". For that you just need to seperate value (dark, medium, light).
Look at this quilt by QB member Ninnie for another great inspiration for scrap quilts.
http://www.quiltingboard.com/t-50718-1.htm