Or, really, any hat, but isn't it more fun if it's Lilly Dache or Mr. John than a cheap felt number from "one size fits all"?
Left, the modern take, a shot from the February American Vogue by Stephen Meisel. The models' stylized strut is perfectly complemented by the tilt of their hats. The angle is everything. The dynamism of a diagonal brings vivacity and interest that acts like a magnet on the eye.
Below, in the vintage version, is the same principle at work. Check out the gal center, back row. Her angle is spot on. Looking good, Mom!
There is nothing at all wrong with standing in front of a mirror and experimenting with hat pitches and yaws until you find the one that best suits your face and the shape of the brim/crown. It's not vanity, it's aesthetics, and that counts.