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That is why you use stocking stitch -- because you want it to curl. If you don't, then you have to make some adjustments.

The knitting will curl because you have uneven forces in the knit stitch (a purl is only the reverse of a knit) That is, the front of a knit stitch tends to want to pull forward, while the back tends to push outwards. The combined forces from front and back will cause the fabric to curl towards the knit side. Scarves will curl upwards.

This same situation also causes the sides to curl outwards!

The solution is to have even forces along the edges. That is, you need the same number of knits and purls. That is why garter stitch is a good thing to use for borders on scraves. You can also use garter stitch along the edges too. You don't need much -- as few as 1, 2 or 3 stitches usually will do it. You can also use other stitch patterns that uses equal knit and purls such as moss stitch, or seed stitch, or rib.

You can use this to your advantage in some situations, such as the roll brim hat, or the rolled collar and cuffs on sweaters or socks.

Here's a link to TechKnitter's blog, which gives you a much more thorough explanation of what's going on. Particularly helpful may be the links at the end of the post, a four-part series in which she explores solutions to the same problem you're facing.

http://techknitting.blogspot.com/2007/03/mysteries-of-knitting-part-1-tale-of.html

I love using good old stockinette in something that doesn't have 'edges'... like a hat that wraps around continuously, or a sweater panel or afghan square that may be seamed to pieces on either side. Basically, as has been said, the hard reality of stockinette is that it's just not comfortable flying solo in a flat piece of knitting. He needs a friend to keep him straight. The types of friends that come to his aid are many and varied.

I sound weird, talking about knitting like that. Forgive me.

If you like the look of stockinette but need a standalone piece that doesn't curl on itself, a couple of similar-looking options would be double-knitting (ending up as if you had magically fused the ends into a continuous tube and pressed it flat) or --believe it or not-- K1, P1 ribbing. The latter is completely balanced ribbing and will not curl at all, but it pulls in on itself so much that it looks very similar to stockinette. This is a great option for a scarf, though it is a pain until your patience for ribbing increases. Eventually, you may find 1x1 ribbing as mindless as stockinette.

Hi Dennis,
Stockinette stitch does curl because of the type of stitch it is. If you use a garter stitch for a few rows at the start of a scarf and then four or five stitches at the beginning of a row and then at the end of a row, that should do the trick. I find that when I make scarves, I like to do a rib stitch, such as K2, P2 all across the row. I just finished one using that combo of stitches and it didn't curl at all. I also use the K2,P2 when knitting the first 2 inches or so of a stocking hat using circular needles and then just knit all around and around and around. I am a beginning myself, knitting just since this past September and found the rolling frustrating as well. Of course, some like the rolling effect on a hat, scarf, or neck of a sweater. I hope this helps.
Mark