+1  A: 

A couple of points to note

1) You need to be targeting an actual property of Border - You are in effect trying to target the value (DropShadowEffect) of the Effect property, not the property itself.

2) You need to sort the syntax of the PropertyPath.

Change your Storyboard.Target property to the following and you should be fine:

Storyboard.TargetProperty="(Effect).Opacity"

EDIT Working code as noted in comment:

<Border BorderThickness="10" Height="100" Width="100">
    <Border.BorderBrush>
        <SolidColorBrush Color="Red"></SolidColorBrush>
    </Border.BorderBrush>
    <Border.Style>
        <Style TargetType="Border">
            <Style.Resources>
                <Storyboard x:Key="GlowOn">
                    <DoubleAnimationUsingKeyFrames BeginTime="00:00:00" 
                          Storyboard.TargetProperty="(Effect).Opacity">
                        <SplineDoubleKeyFrame KeyTime="0:0:0.3" Value="1"/>
                    </DoubleAnimationUsingKeyFrames>
                </Storyboard>
                <Storyboard x:Key="GlowOff">
                    <DoubleAnimationUsingKeyFrames BeginTime="00:00:00" 
                          Storyboard.TargetProperty="(Effect).Opacity">
                        <SplineDoubleKeyFrame KeyTime="0:0:0.3" Value="0"/>
                    </DoubleAnimationUsingKeyFrames>
                </Storyboard>
            </Style.Resources>

            <Setter Property="CornerRadius" Value="6,1,6,1" />
        <!--<Setter Property="BorderBrush"
                    Value="{StaticResource SelectedBorder}" />-->
            <Setter Property="BorderThickness" Value="1" />
        <!--<Setter Property="Background"
                    Value="{StaticResource DeselectedBackground}" />-->
            <Setter Property="RenderTransformOrigin" Value="0.5,0.5" />
        <!--<Setter Property="TextBlock.Foreground"
                    Value="{StaticResource SelectedForeground}" />-->

            <Setter Property="RenderTransform">
                <Setter.Value>
                    <RotateTransform Angle="90"/>
                </Setter.Value>
            </Setter>

            <Setter Property="Effect">
                <Setter.Value>
                    <DropShadowEffect ShadowDepth="20"
                                      BlurRadius="8"
                                      Color="#FFB0E9EF"/>
                </Setter.Value>
            </Setter>

            <Style.Triggers>
                <Trigger Property="IsMouseOver" Value="True">

                    <Trigger.EnterActions>
                        <BeginStoryboard
                              Storyboard="{StaticResource GlowOn}"/>
                    </Trigger.EnterActions>

                    <Trigger.ExitActions>
                        <BeginStoryboard
                              Storyboard="{StaticResource GlowOff}"/>
                    </Trigger.ExitActions>

                </Trigger>
            </Style.Triggers>

        </Style>
    </Border.Style>
</Border>
Simon Fox
I get an InvalidOperationException because Effect doesn't have an Opacity property. The value of Effect is DropShadowEffect which has the Opacity property I'm trying to target, but as you point out my XAML is wrong.I've tried setting x:Name on the DropShadowEffect but you can't use TargetName in Styles.There’s a hole in the MSDN documentation about the use of these brackets in storyboards, but I tracked it down in the help for PropertyPath. However I still can't solve the problem. I think I need to cast Effect to DropShadowEffect but this doesn’t seem possible in XAML.Any other ideas?
Zodman
I managed to get the code you have posted working using the syntax I have provided, I did this in a stripped back sample app. I will post what I used and you can maybe work back from that...
Simon Fox
Note I have removed the setters which use static resources that you have not provided but that is not going to effect the demonstration. And I notice you are trying to set TextBlock.Foreground property within your style which also will not work.
Simon Fox
....and I have increased the drop shadow depth to exagerate the effect...
Simon Fox
Correction: You were right after all.I used Blend to generate the Storyboard XAML for me - “Effect.(DropShadowEffect.Opacity)”.I still had problems though. To cut a long story short, I had moved the setter for the Effect to the Trigger at some point, which was the cause of the InvalidOperationException (as the effect wasn’t there when the mouse moved off the border). Moving this setter back into the Style (as I had said in the original post) and it all worked.I then changed the Storyboard to “(Effect).Opacity” as you suggested and it worked. Thanks heaps Simon!
Zodman