Why don't the items in my ItemsControls layout horizontally?

Wrong way around. Customize the panel that the ItemsControl uses to contain its items:

<ItemsControl>
    <ItemsControl.ItemsPanel>
        <ItemsPanelTemplate>
             <StackPanel Orientation="Horizontal"/>
        </ItemsPanelTemplate>
    </ItemsControl.ItemsPanel>
</ItemsControl>