Stockinette, for example, a basic and commonly used stitch made from alternating knitted rows with purled ones, always tends to curl at the edges. (In fact, many knitting patterns are written to take advantage of this.) A lightweight yarn will emphasize this curl, while a heavier yarn will minimize the effect.
Also, if you cast-on and cast-off stitches -- the stitches you use to begin and end a garment -- are tighter than the rest of the knitting, you will more likely encounter curling at the ends of the piece. You can alleviate the problem somewhat by blocking the finished scarf.
To do this, lay it on a padded ironing board, pull at the edges so the whole piece lies flat and pin it in place. Spray a linen towel or dishcloth with water until it is quite damp, and lay the towel on top of the scarf.
Then press the fabric with a steam iron on a high setting (never press directly onto a knitted piece with a hot iron). The heat and steam will stretch the yarn somewhat, relaxing the tension that leads to curling. Do not unpin the scarf until it is completely cool and dry.
Blocking is a good finishing technique for nearly any hand-knitting. It helps to smooth seams and give the whole piece a neater, more professional look. You should not expect it to completely uncurl a stockinette-stitched scarf, however. To further reduce curling, you might try adding a decorative crocheted edge or a trimming of ribbon to the finished scarf.
In the future, try knitting a garter-stitch (knit only) border for several rows on a stockinette scarf, or knit the whole thing in a stitch that does not present a curling problem, such as ribbing (alternating knits and purls, stitch by stitch).
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