Is it possible to change the busy animation in the

Is it possible to change the busy animation in the Busyindicator of Extended WPF Toolkit? In particular, I would like to change it to a .gif animation.

Yes, of course. You can define your own custom content (documentation).

Busy indicator custom content example:

 <xctk:BusyIndicator IsBusy="True" DisplayAfter="0">
       <xctk:BusyIndicator.BusyContentTemplate>
            <DataTemplate>
                 <StackPanel Margin="4">
                          <TextBlock Text="Downloading Email" FontWeight="Bold" HorizontalAlignment="Center"/>
                           <StackPanel Margin="4">
                               <TextBlock Text="Downloading message 4/10..."/>
                               <ProgressBar Value="40" Height="15"/>
                           </StackPanel>
                           <Grid>
                               <Grid.ColumnDefinitions>
                                   <ColumnDefinition/>
                                   <ColumnDefinition/>
                               </Grid.ColumnDefinitions>
                               <Button Grid.Column="0" Content="Pause" HorizontalAlignment="Right" Margin="0 0 2 0"/>
                               <Button Grid.Column="1" Content="Cancel" HorizontalAlignment="Left" Margin="2 0 0 0"/>
                           </Grid>
                  </StackPanel>
            </DataTemplate>
       </xctk:BusyIndicator.BusyContentTemplate>
       <xctk:BusyIndicator.OverlayStyle>
                  <Style TargetType="Rectangle">
                        <Setter Property="Fill" Value="#ffffeeee"/>
                  </Style>
       </xctk:BusyIndicator.OverlayStyle>
       <xctk:BusyIndicator.ProgressBarStyle>
                   <Style TargetType="ProgressBar">
                            <Setter Property="Visibility" Value="Collapsed"/>
                   </Style>
       </xctk:BusyIndicator.ProgressBarStyle>
       <ContentControl Style="{StaticResource SampleContent}"/>
</xctk:BusyIndicator>

To display animated GIF images in WPF you can use WPF Animated GIF.

Busy indicator with animated GIF:

<xctk:BusyIndicator IsBusy="True" DisplayAfter="0">
    <xctk:BusyIndicator.BusyContentTemplate>
        <DataTemplate>
            <StackPanel Margin="5">                   
                <Image gif:ImageBehavior.AnimatedSource="loading.gif" Width="100" Height="100" />
            </StackPanel>
        </DataTemplate>
    </xctk:BusyIndicator.BusyContentTemplate>
    <xctk:BusyIndicator.OverlayStyle>
        <Style TargetType="Rectangle">
            <Setter Property="Fill" Value="#ffffeeee"/>
        </Style>
    </xctk:BusyIndicator.OverlayStyle>
    <xctk:BusyIndicator.ProgressBarStyle>
        <Style TargetType="ProgressBar">
            <Setter Property="Visibility" Value="Collapsed"/>
        </Style>
    </xctk:BusyIndicator.ProgressBarStyle>
    <ContentControl />
</xctk:BusyIndicator>