Sample ListBox (XAML) where Drag originates:

<ListBox Name="lstEnvironments" 
               SelectionChanged="lstEnvironments_SelectionChanged" 
               PreviewMouseLeftButtonDown="lstEnvironments_PreviewMouseLeftButtonDown" 
               MouseMove="lstEnvironments_MouseMove">
          <ListBoxItem>Normal</ListBoxItem>
          <ListBoxItem>Restaurant/Party</ListBoxItem>
          <ListBoxItem>Telephone</ListBoxItem>
          <ListBoxItem>Music</ListBoxItem>
</ListBox>

Code behind:

private void lstEnvironments_SelectionChanged(object sender, SelectionChangedEventArgs e)
{
    string myDragData = ((ListBoxItem)lstEnvironments.SelectedItem).Content.ToString();
    lblSelectedEnvironment.Text = string.Format("{0}", myDragData);  // selected data
}
 
private void lstEnvironments_PreviewMouseLeftButtonDown(object sender, MouseButtonEventArgs e)
{
    // Store the mouse position
    startPoint = e.GetPosition(null);
}
 
private void lstEnvironments_MouseMove(object sender, MouseEventArgs e)
{
    // Get the current mouse position
    Point mousePos = e.GetPosition(null);
    Vector diff = startPoint - mousePos;
 
    if (e.LeftButton == MouseButtonState.Pressed &&
        Math.Abs(diff.X) > SystemParameters.MinimumHorizontalDragDistance &&
        Math.Abs(diff.Y) > SystemParameters.MinimumVerticalDragDistance)
    {
        // Get the dragged ListBoxItem
        ListBox lstBox = sender as ListBox;
        ListBoxItem lstBoxItem = FindAnchestor<ListBoxItem>((DependencyObject)e.OriginalSource);
 
        // Find the data behind the ListBoxItem
        //string str = (string)lstBox.ItemContainerGenerator.ItemFromContainer(lstBoxItem);
        string str = ((ListBoxItem)lstBox.SelectedItem).Content.ToString();
 
        // Initialize the drag & drop operation
        DataObject dragData = new DataObject(typeof(string), str);
        DragDrop.DoDragDrop(lstBoxItem, dragData, DragDropEffects.Move);
    } 
}
 
// Helper to search up the VisualTree
private static T FindAnchestor<T>(DependencyObject current)
    where T : DependencyObject
{
    do
    {
        if (current is T)
        {
            return (T)current;
        }
        current = VisualTreeHelper.GetParent(current);
    }
    while (current != null);
    return null;
}

Target controls where Drop is performed. In this case, a ListBox, TextBlock, and TextBox.

<TextBlock FontWeight="Bold" Margin="0,10,0,0">Dragged Items</TextBlock>
<TextBlock>ListBox:</TextBlock>
<ListBox Name="lstAppliedEnvironment" AllowDrop="True" Height="100"  SelectionMode="Single"
         DragEnter="lstAppliedEnvironment_DragEnter"
         Drop="lstAppliedEnvironment_Drop">
</ListBox>
<StackPanel Orientation="Horizontal">
    <TextBlock>TextBlock:</TextBlock>
    <TextBlock Name="lblAppliedEnvironment" Margin="5,0,0,20" AllowDrop="True"
           DragEnter="lblAppliedEnvironment_DragEnter" Drop="lblApliedEnvironment_Drop">Value</TextBlock>
</StackPanel>
<TextBox Name="txtAppliedEnvironment" Height="30" AllowDrop="True" 
         DragEnter="txtSelectedEnvironment_DragEnter" 
         Drop="txtAppliedEnvironment_Drop"></TextBox>

Code behind:

private void lstAppliedEnvironment_DragEnter(object sender, DragEventArgs e)
{
    if (!e.Data.GetDataPresent("str") || sender == e.Source)
    {
        e.Effects = DragDropEffects.None;
    }
}
 
private void lstAppliedEnvironment_Drop(object sender, DragEventArgs e)
{
    if (e.Data.GetDataPresent(typeof(string)))
    {
        string str = e.Data.GetData(typeof(string)) as string;
        ListBox lstBox = sender as ListBox;
        lstBox.Items.Add(str);
    }
}
 
private void lblAppliedEnvironment_DragEnter(object sender, DragEventArgs e)
{
    if (!e.Data.GetDataPresent("str") || sender == e.Source)
    {
        e.Effects = DragDropEffects.None;
    }
}
 
private void lblAppliedEnvironment_Drop(object sender, DragEventArgs e)
{
    if (e.Data.GetDataPresent(typeof(string)))
    {
        string str = e.Data.GetData(typeof(string)) as string;
        TextBlock lbl = sender as TextBlock;
        lbl.Text = str;
    }
}

• Drag and Drop in WPF
• Drag and Drop in WPF Explained End to End (Jaime Rodríguez)
• MSDN: Drag and Drop Overview
• WPF Tutorial: Drag and Drop
• WinForms using custom cursors with Drag and Drop
• Dragging Elements in Canvas