I came across this page looking for the same answer as the original author, and proving there's always more than one way to do it, the solution for me was even easier than the answers provided here so far, so I figured I might as well add to the pile.
The motivation for the binding is to keep it nice & MVVM. The probable usage of the ViewModel is to have a property w/ a name such as "CurrentThingy", and somewhere else, the DataContext on some other thing is bound to "CurrentThingy".
Rather than going through additional steps required (eg: custom behavior, 3rd party control) to support a nice binding from the TreeView to my Model, and then from something else to my Model, my solution was to use simple Element binding the other thing to TreeView.SelectedItem, rather than binding the other thing to my ViewModel, thereby skipping the extra work required.
XAML:
<TreeView x:Name="myTreeView" ItemsSource="{Binding MyThingyCollection}">
.... stuff
</TreeView>
<!-- then.. somewhere else where I want to see the currently selected TreeView item: -->
<local:MyThingyDetailsView
DataContext="{Binding ElementName=myTreeView, Path=SelectedItem}" />
Of course, this is great for reading the currently selected item, but not setting it, which is all I needed.