Slight to medium curve depending on the hat. My problem is that my head is so damn big I can't find one that fits me right. Seriously, I have a Hagersburg Suns hat that is a size 8... yeah 8 and it's snug on my freakin' melon
Hopefully my head will shrink enough with weight loss that I'll be able to wear a L/XL Flexfit hat again... sigh...