I love a good braided cable, and I've found myself drawn over and again to hats with a braided cable edge! (see my recently finished Cable Hat with Flower as an example) Many times, the rest of the hat is rather plain, but the sideways braid at the edge is always enough to make the hat look fancy and gorgeous.
From left to right, here's a few hats I'm loving right now, with a variety of braided cable edges.
Coronet - Perfect for someone new to braided cables, this hat is simple stockinette after you master the gorgeous cabled braid at the brim.
Saxon Braided Cabled Cap - This more detailed braided edge is large and gorgeous. The detail makes the braid a focal point for the hat!
Teampall Bhreacháin Hat - The all-over braiding on this hat means I wouldn't be able to knit it while reading a book or even watching a movie, but the finished result is worth the focused effort!
Wavy Moss Hats and Headband - I love knitting the moss stitch, and I'm in heaven that this pattern has a few varieties, both of hat types and a headband as well!