Example mod (item would be registered as standard, and not rendered when equipped)

ItemInvisArmour

import net.minecraft.item.ItemArmor;
import net.minecraft.item.ItemStack;


/**
 * @author Alpvax
 *
 */
public class ItemInvisArmour extends ItemArmor
{
	public ItemInvisArmour(ItemArmor.ArmorMaterial material, int renderIndex, int armorType)
	{
		super(material, renderIndex, armorType);
	}
	public String getName()
	{
		return "exampleArmour";
	}
	
	@Override
	public float getItemVisibility(ItemStack stack)
	{
		return 0.0F;//Invisible to mobs
	}
}