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>

Another nice approach can be seen here: http://blogs.microsoft.co.il/blogs/eladkatz/archive/2011/05/29/what-is-the-easiest-way-to-set-spacing-between-items-in-stackpanel.aspx Link is broken -> this is webarchive of this link.

It shows how to create an attached behavior, so that syntax like this would work:

<StackPanel local:MarginSetter.Margin="5">
   <TextBox Text="hello" />
   <Button Content="hello" />
   <Button Content="hello" />
</StackPanel>

This is the easiest & fastest way to set Margin to several children of a panel, even if they are not of the same type. (I.e. Buttons, TextBoxes, ComboBoxes, etc.)