<ListView Name="MyListView">
    <ListView.View>
        <GridView>
            <GridViewColumn Header="Foo" DisplayMemberBinding="{Binding Foo}"/>
            <GridViewColumn Header="Bar" DisplayMemberBinding="{Binding Bar}"/>
        </GridView>
    </ListView.View>
</ListView>

var foobars = new ObservableCollection<Foobar>();
foobars.Add(new Foobar { Foo = "Hello", Bar = "world" });
MyListView.ItemsSource = foobars;

var word = (string)(((ListViewItem)MyListView.Items[0]).SubItems[1]);

var word = ((Foobar)MyListView.Items[0]).Bar;

var columns = ((GridView) MyListView.View).Columns;
var foobar = (Foobar)MyListView.Items[0];
var result = (string)DataBinder.Eval(foobar, (Binding) columns[0].DisplayMemberBinding);

public class DataBinder
{
    private static readonly DependencyProperty BindingEvalProperty = DependencyProperty.RegisterAttached(
        "BindingEval",
        typeof(Object),
        typeof(DependencyObject),
        new UIPropertyMetadata(null));

    public static Object Eval(Object data, Binding binding)
    {
        var newbinding = new Binding {Path = binding.Path, Converter = binding.Converter, Source = data};
        var evalobj = new DependencyObject();
        BindingOperations.SetBinding(evalobj, BindingEvalProperty, newbinding);
        return evalobj.GetValue(BindingEvalProperty);
    }
}