Object origins hold a lot of vital information, such as an object's scale, rotation, and position. You'll want to apply the scale, and rotation of the object, or it will likely be horribly disfigured after export.
To apply scale and rotation in blender, select the object and press CTRL+A in Object Mode, and select the respective options in the menu.
If the object is rigged to the body, the origin of the object should be in the exact location of the body's origin. As for hats and other non-rigged head-worn items, the origin should be placed in the middle of the head bone.
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If you are using the human rigging template in the SS3D Modeler's Template, you can use the included objects as reference for where the origin should go.