It's a great way to practice pattern stitches. If you have a stitch dictionary, just pick a pattern you like and knit up a swatch. Borders are nice, especially if you are using a pattern that tends to curl. Garter and moss stitch make nice borders.
As others have pointed out, 100 percent cotton is best and the three big manufacturers are Peaches and Cream, Sugar and Cream and Lion. Cottontots is also an option and makes a very soft cloth. Some people use cotton blends like Aunt Lydia's denim.
Knittingpatterncentral.com has links to a lot of washcloths and dishcloths.