Multiline for WPF TextBox
Also, if, like me, you add controls directly in XAML (not using the editor), you might get frustrated that it won't stretch to the available height, even after setting those two properties.
To make the TextBox stretch, set the Height="Auto".
UPDATE:
In retrospect, I think this must have been necessary thanks to a default style for TextBoxes specifying the height to some standard for the application somewhere in the App resources. It may be worthwhile checking this if this helped you.