Ah, that's an age-old topic. How to make a knitted scarf that won't curl on the edges.
Well, the easy answer is to use a stitch pattern that uses an equal distribution of knits and purls. For example, garter stitch, 2/2 ribbing, 1/1 ribbing, seed stitch, or moss stitch.
And those non-curling stitch patterns can make lovely scarves. Cast on in a multiple of 4 plus 2 (e. g., 34) stitches, and work in 2/2 ribbing for a warm, non-curling, and very traditional scarf. Great for guys.
However, what you might find is this:
A scarf made from a vertical non-curling stitch pattern (e. g,, 2/2 ribbing) will, with wear, stretch vertically. So, it might start out 6 inches wide after blocking and end up being 4 inches wide with wear. So keep that in mind when you're casting on.
A scarf made from a horizontal non-curling stitch pattern (e. g., garter stitch) will not necessarily drape the way you want it to. It might be a bit rigid.
A partial solution is to add non-curling stitches around all four edges of the scarf. This is somewhat effective (and this is usually what I do). But, because a scarf is being stretched vertically all the time (with gravity, with knotting, with pulling) it will eventually start to curl.
And I'd like it be considered that a flat, non-curling, rigid scarf is not 100% desirable. A little drape, a little curl, helps to give knitted fabric a little character.
But don't despair. 1) Learn to embrace the curl. That's the nature of knits. 2) When the scarf gets too curled, wet block it. It probably could use a wash by then. 3) Try a thinner, wider wrap (like Paravel) or a triangular shawl worn as a scarf. It's a more versatile accessory, and the longer rows relieve some of the knitting tension, making a flatter fabric.
BTW: The incomparable TECHknitter has a great post explaining why stockinette curls. She also has a couple of solutions for finished scarves: try making ribbing by dropping columns of stitches, or line a scarf with fabric.
