In the Rectangle properties window, go down to the Miscellaneous section and their is an Effect property. Select New and you can select a BlurEffect
You need to be aware that this can have a negative impact on performance, particularly if the PC doesn't have a good graphics card. Also, at the moment, the BitmapEffect is not supported in Silverlight, so you would have to blur it in another graphics program and just display an image.
The resulting XAML looks like this:
<Rectangle Fill="#FFFFFFFF" Stroke="#FF000000" HorizontalAlignment="Left" Margin="56,172,0,0" VerticalAlignment="Top" Width="107" Height="36">
<Rectangle.Effect>
<BlurEffect/>
</Rectangle.Effect>
</Rectangle>