Want the truth? The cold, hard truth?
"Help," the knitter posts to an online forum. And help people do, or attempt to. One person will advise adding a crocheted edge. Another will advocate working the first and last few stitches in garter stitch next time. A third person will suggest picking up the stitches along the edge and working a border in ribbing. Yet another person will swear that an aggressive blocking will do the trick.
Want the truth? The cold, hard truth? None of these things will work. Believe me, I have tried them all.
Stockinette curls because of the way the knit stitch looks in 3D. Imagine one single stitch, magnified and hovering in mid-air. The purl side has a bar. The knit side has a big V. The V of the knit side is much bigger than the purl-side bar. Thus, there is more fabric on the knit side than on the purl side.
Stack up enough of these knit stitches, and the knit side - being larger - forces the fabric to curl. There is no way around it, it's just a factor of the actual shape of the fabric.
This is why, when choosing a stitch pattern for a scarf, you want as even a distribution of knits and purls on each side as possible. It's also why no amount of edging or border will ever be able to tame the curl. And sure, you can flatten the bejeezus out of it with a steam iron, but the curl will always return because the fabric will slowly return to shape.
There are only a few ways to fix a finished scarf that's curling. TechKnitter has the only three solutions: drop columns of stitches, drop stitches and re-knit them as ribbing, and sew on a fabric lining.
If you are thinking about knitting a scarf in stockinette, your best solution will be to either knit it in the round, or knit it at double the width and seam it together when you're done. Granted this means you will have to knit twice as much scarf. But the results will be worth it! I knit a stockinette tube scarf in the round a few months ago, and it went really fast!)