You could just make it into a TextBox that's Read Only which just looks like a TextBlock, kind of like;
<Style x:Key="ReadOnlyTextBox" TargetType="TextBox">
<Setter Property="IsReadOnly" Value="True" />
<Setter Property="Padding" Value="5"/>
<Setter Property="Margin" Value="0"/>
<Setter Property="Background" Value="Transparent"/>
<Setter Property="BorderBrush" Value="Transparent"/>
<Setter Property="BorderThickness" Value="0"/>
<Setter Property="IsTabStop" Value="False"/>
<Setter Property="HorizontalScrollBarVisibility" Value="Disabled"/>
<Setter Property="VerticalScrollBarVisibility" Value="Disabled"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="TextBox">
<Grid x:Name="RootElement">
<ScrollViewer x:Name="ContentElement"
Margin="{TemplateBinding Margin}"
Background="{TemplateBinding Background}"
BorderBrush="{TemplateBinding BorderBrush}"
BorderThickness="{TemplateBinding BorderThickness}"
IsTabStop="{TemplateBinding IsTabStop}"
Padding="{TemplateBinding Padding}"
HorizontalScrollBarVisibility="{TemplateBinding HorizontalScrollBarVisibility}"
VerticalScrollBarVisibility="{TemplateBinding VerticalScrollBarVisibility}"/>
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
The ScrollViewer ContentElement would be in a TextBox by default, you could substitute for a ContentPresenter instead if you like also.
Then put it into effect;
<TextBox Text="Blah Blah Blah you can copy me!" Style="{StaticResource ReadOnlyTextBox}"/>
Hope this helps!
ADDENDUM: As @doodleus pointed out in the comments. Template binding the Content Property within the template may be necessary. As "ContentElement" is a named part of the Silverlight TextBox control. One of the little nuance differences to watch for in the different xaml Variants. I must not have paid attention to the Tags when I originally created the example. So kudos to him for correcting me.
