The Loom Muse : Chunky Cable Hat
Very Simple Spiral Hat FREEPattern with Step by Step Video Tutorial for the Circular Loom. Easy enough for beginners.
Tweed Beanie hat knitting loom pattern, all in one loom
Lady By The Bay: Seed/Moss Stitch Knitted Hat Pattern
This is a great pattern for someone who is new to colorwork.
Loom knit hat for beginners More
How to add a liner to your crocheted hats: A tutorial to help you get cozy by Playin' Hooky Designs
How to Loom Knit a Faux Braid (No Bind off or cast on)
Craft Knitting Loom