Hats can be useful when you can't wear heavy armor.

A couple hats have out of battle effects.

HELMETS

    Mysterious Hat
        sell = 6
        def = 1
        classes = Wizard, Fighter, Pilgrim, Merchant, GoofOff, Sage
        info = A hat that is said to increase magic power.
    Noh Mask
        sell = 1
        def = 1
        classes = Hero, Soldier, Wizard, Fighter, Pilgrim, Merchant, GoofOff, Sage
        info = A hat with a sence of ill fate around it.
    Leather Helmet
        buy = 80
        sell = 55
        def = 2
        classes = Hero, Soldier, Pilgrim, Merchant, GoofOff, Sage
    Hat of Wind
        def = 5
        sell = 100
        classes = Hero, Soldier, Pilgrim, Wizard, Fighter, Merchant, GoofOff
        info = This hat has the power to return you to the last town you visited.
    Hermes Hat
        def = 10
        sell = 1000
        classes = Hero, Soldier, Pilgrim, Wizard, Fighter, Merchant, GoofOff
        info = This hat has the power of the Return spell built in.
    Wooden Hat
        buy = 120
        sell = 60
        def = 6
        classes = Hero, Soldier, Pilgrim, Merchant, Sage
    Feather Hat
        buy = 280
        sell = 160
        def = 8
        classes = Wizard, Pilgrim, Merchant, GoofOff, Sage
    Turban
        buy = 160
        sell = 80
        def = 8
        classes = Merchant, GoofOff
    Zenithian Helm
        def = 12
        classes = Hero
        info = Part of the Zenithian equipment set.
    Lucky Band
        def = 12
        sell = 1000
        classes = Hero, Soldier, Pilgrim, Wizard, Fighter, Merchant, Sage, GoofOff
        info = This hair band will give you many benefits as you walk around.
    Iron Helmet
        buy = 1000
        sell = 600
        def = 16
        classes = Hero, Soldier, Pilgrim, Sage
    Iron Mask
        buy = 3500
        sell = 2000
        def = 20
        classes = Hero, Soldier
    Ortegas Helmet
        def = 28
        classes = Hero
        info = A helmet said to have belonged to the great hero,  Erdrick.
    Mage Hat
        def = 33
        buy = 14000
        sell = 9000
        classes = Wizard, Pilgrim, Sage
    Unlucky Helmet
        def = 35
        classes = Soldier
        info = A helmet surrounded in ill fate.
    Silver Helm
        def = 43
        buy = 20000
        sell = 14000
        classes = Hero, Soldier, Merchant
    Metal Babble Helm
        def = 50
        classes = Hero, Soldier, Pilgrim, Merchant, Sage
        info = Strongest Helmet in the world.