A very similar version of this pattern appears in Charmed Knits on page 70.
Formerly available at knit atypically website. Also available at the forum for The Leaky Cauldron, Leaky Lounge, here.
Stockinette scarf knit in the round on 16" circular needles.
Unger Utopia (100% acrylic): US9 / 5.5mm
Plymouth Encore Worsted (25% wool, 75% acrylic): US8 / 5.0 mm
Brown Sheep Nature Spun Worsted (100% wool): US7 / 4.5 mm
Possible color choices for each house can be found on the pattern website.
Uses at least 400 yards of each color. Many knitters have cast on fewer stitches than recommended.
From the pattern website:
Hogwarts scarves have nineteen stripes: ten dark stripes and nine light ones, and they begin and end in a dark stripe. Each end has eleven bunches of fringe: six dark and five light, again with dark fringe on both edges.
I tend to like big scarves, and if you watch closely in the movies, Hogwarts scarves are big. For adults, I usually aim for 65-70" long and 7-8" wide. That means each stripe is a little over three inches long. Kids' scarves, of course, should be smaller, depending on their age. I've found that a stripe width-to-height ratio of 2:1 to 2.5:1 looks about right.
The scarves are knit in stockinette stitch as tubes. It's not as scary as it sounds - it means each scarf takes twice as much time and yarn to make, but it's also twice as warm, has no 'wrong' side, and doesn't curl the way a single piece of stockinette knitting will. Knitting in the round is very much the same as straight-needle knitting. There are two things you'll need to be careful about: that you pull the cast-on row closed tightly when joining, and that the row isn't twisted around the needle (otherwise you'll have to rip back to the beginning and start over). You'll also want to be sure that you cast on twice the number of stitches as your final width dictates. When finished, the tube is flattened, and each end is closed with fringe.