Following are some of my efforts at knitting and crocheting beanies and scarves.
The above child's beanie and scarf are a very simple pattern. The beanie is a straight knit4-purl4 rib until you get the right length (about 24 cm), gather the stitches straight off the needles, pull tight and stitch the seam together. No shaping, no casting off, very easy. The scarf is the same knit4-purl4 rib until you get to the desired length.
The scarf for the above combo was an experiment with doing a crocheted rib. It uses treble crochet (US dc) going around the post alternating front and back. I decided to crochet this one length-ways so that I could ensure that it was an appropriate length. I wasn't particularly worried about the width so I just kept going until I ran out of wool.
Another wool creation and another experiment. Sue and I were taught this stitch a couple of years ago and I had speculated on its suitability for a scarf and I think it worked out nicely.
Another simple knit4-purl4 rib creation, this time in acrylic. This one does have some shaping towards the top, but only until it's reduced to about 12 stitches, these are then gathered off the needles the same as the child's beanie above.
Another wool combo, I especially like the autumn tones in this one and the way the colours stripe instead of being in patches. The beanie was done the same as the first one except that I shaped the top.