Crocheting Patterns:
Lattice Hat-This hat is really pretty, but it's definitely not for beginners. Also, it's very thick, so try to use thinner yarn.
Addison Hat-This hat is pretty too, and it's relatively easy, although it's pretty repetitive.
Bev's Bear Beanie-As the name might indicate, this hat is made to look like a bear. It's really cute and creative, and it's guaranteed to brighten anyone's day.
Headhuggers-This site has some really great patterns for both knit and crocheted hats.
Kitty Cat Hat-My own creation; loosely inspired by Bev's Bear Beanie.Bunny Rabbit Hat-My mom made this one on vacation after we found the bear hat. It's soooooooooo cute.
Ribbed Cap– I haven't made this one, but it looks like it's nice and relatively easy
Crochet Pattern Central-This site has a bunch of good hats. Not all of them would work for chemocaps though. Try to avoid the ones with seams, and if they use a scratchy or very thick yarn, use a different type.
Way Too Colorful Hat-I haven't tried this one yet either, but it looks really nice.
Knitting Patterns:
Bev's Country Cottage–This is the website that the bear beanie came from. It's got lots of knitting patterns. I haven't tried these out, but I bet they're good.
Headhuggers-This site has some really great patterns for both knit and crocheted hats. The eyelet rolled brim knit hat is really pretty.