How do I space out the child elements of a StackPanel?

Use Margin or Padding, applied to the scope within the container:

<StackPanel>
    <StackPanel.Resources>
        <Style TargetType="{x:Type TextBox}">
            <Setter Property="Margin" Value="0,10,0,0"/>
        </Style>
    </StackPanel.Resources> 
    <TextBox Text="Apple"/>
    <TextBox Text="Banana"/>
    <TextBox Text="Cherry"/>
</StackPanel>

EDIT: In case you would want to re-use the margin between two containers, you can convert the margin value to a resource in an outer scope, f.e.

<Window.Resources>
    <Thickness x:Key="tbMargin">0,10,0,0</Thickness>
</Window.Resources>

and then refer to this value in the inner scope

<StackPanel.Resources>
    <Style TargetType="{x:Type TextBox}">
        <Setter Property="Margin" Value="{StaticResource tbMargin}"/>
    </Style>
</StackPanel.Resources>