Solution 1:

Interesting blog post here: Dispose of a WPF UserControl (ish)

It mentions subscribing to Dispatcher.ShutdownStarted to dispose of your resources.

Solution 2:

Dispatcher.ShutdownStarted event is fired only at the end of application. It's worth to call the disposing logic just when control gets out of use. In particular it frees resources when control is used many times during application runtime. So ioWint's solution is preferable. Here's the code:

public MyWpfControl()
{
     InitializeComponent();
     Loaded += (s, e) => { // only at this point the control is ready
         Window.GetWindow(this) // get the parent window
               .Closing += (s1, e1) => Somewhere(); //disposing logic here
     };
}

Solution 3:

You have to be careful using the destructor. This will get called on the GC Finalizer thread. In some cases the resources that your freeing may not like being released on a different thread from the one they were created on.

Solution 4:

I use the following Interactivity Behavior to provide an unloading event to WPF UserControls. You can include the behavior in the UserControls XAML. So you can have the functionality without placing the logic it in every single UserControl.

XAML declaration:

xmlns:i="http://schemas.microsoft.com/expression/2010/interactivity"

<i:Interaction.Behaviors>
    <behaviors:UserControlSupportsUnloadingEventBehavior UserControlClosing="UserControlClosingHandler" />
</i:Interaction.Behaviors>

CodeBehind handler:

private void UserControlClosingHandler(object sender, EventArgs e)
{
    // to unloading stuff here
}

Behavior Code:

/// <summary>
/// This behavior raises an event when the containing window of a <see cref="UserControl"/> is closing.
/// </summary>
public class UserControlSupportsUnloadingEventBehavior : System.Windows.Interactivity.Behavior<UserControl>
{
    protected override void OnAttached()
    {
        AssociatedObject.Loaded += UserControlLoadedHandler;
    }

    protected override void OnDetaching()
    {
        AssociatedObject.Loaded -= UserControlLoadedHandler;
        var window = Window.GetWindow(AssociatedObject);
        if (window != null)
            window.Closing -= WindowClosingHandler;
    }

    /// <summary>
    /// Registers to the containing windows Closing event when the UserControl is loaded.
    /// </summary>
    private void UserControlLoadedHandler(object sender, RoutedEventArgs e)
    {
        var window = Window.GetWindow(AssociatedObject);
        if (window == null)
            throw new Exception(
                "The UserControl {0} is not contained within a Window. The UserControlSupportsUnloadingEventBehavior cannot be used."
                    .FormatWith(AssociatedObject.GetType().Name));

        window.Closing += WindowClosingHandler;
    }

    /// <summary>
    /// The containing window is closing, raise the UserControlClosing event.
    /// </summary>
    private void WindowClosingHandler(object sender, CancelEventArgs e)
    {
        OnUserControlClosing();
    }

    /// <summary>
    /// This event will be raised when the containing window of the associated <see cref="UserControl"/> is closing.
    /// </summary>
    public event EventHandler UserControlClosing;

    protected virtual void OnUserControlClosing()
    {
        var handler = UserControlClosing;
        if (handler != null) 
            handler(this, EventArgs.Empty);
    }
}