I’m already working on my third baby hat done in this simple way. You just crochet a rectangle which you fold in half right sides facing eachother and then you close one side (sewing or crocheting). In order to hold the hat on babys head you crochet a tie band with chains wich you weave in at the bottom.
I worked the hat in Tunisian crochet. It’s a ribbed pattern in two colors. You can find my tutorial here. Of course you can use any pattern and any yarn colors you want to create the rectangle.
A word about sizing: The length of the crocheted rectangle (or twice the width) should be 3/4 of the heads circumference. If you’re unsure make it bigger! You can always fold the border around the face to make it smaller.
And of course this hat would be also nice for older kids and even grown-ups.