XAML Code

<Canvas x:Name="LayoutRoot" Background="Gray">
    <Rectangle Height="20" Width="40" Fill="Blue"
                MouseLeftButtonDown="Rectangle_MouseLeftButtonDown"
                MouseLeftButtonUp="Rectangle_MouseLeftButtonUp"
                MouseMove="Rectangle_MouseMove" Canvas.Left="109" Canvas.Top="88">
    </Rectangle>
</Canvas>

And here is the C# Code.

//To store the initial location of the control.
private Point _StartPoint = default(Point);
//To check whether user started dragging the control.
private bool _IsMouseCaptured = false;

private void Rectangle_MouseLeftButtonDown(object sender, MouseButtonEventArgs e)
{
    UIElement uiElement = sender as UIElement;
    //Reading the current position
    _StartPoint = e.GetPosition(uiElement);
    //Capturing the Mouse.
    this._IsMouseCaptured = uiElement.CaptureMouse();
}

private void Rectangle_MouseLeftButtonUp(object sender, MouseButtonEventArgs e)
{
    //Releasing the Mouse and setting the variable to false.
    UIElement uiElement = sender as UIElement;
    uiElement.ReleaseMouseCapture();
    this._IsMouseCaptured = false;
}

private void Rectangle_MouseMove(object sender, MouseEventArgs e)
{
    //If the Mouse captured, set the Left and Top values of the control
    if (this._IsMouseCaptured)
    {
        UIElement uiElement = sender as UIElement;
        Canvas.SetLeft(uiElement, (e.GetPosition(this).X - this._StartPoint.X));
        Canvas.SetTop(uiElement, (e.GetPosition(this).Y - this._StartPoint.Y));
    }
}

Here is the code. Seems like it is self explanatory

Imports System.IO
Public Class frmMain

    Private Sub txtEditor_MouseDown(ByVal sender As System.Object, _
                                    ByVal e As System.Windows.Forms.MouseEventArgs) _
                                    Handles txtEditor.MouseDown
        'Initiating the Drag and Drop
        txtEditor.DoDragDrop("", DragDropEffects.Copy)
    End Sub

    Private Sub txtEditor_DragEnter(ByVal sender As System.Object, _
                                    ByVal e As System.Windows.Forms.DragEventArgs) _
                                    Handles txtEditor.DragEnter
        'Ensures the dragging data is valid type.
        'Then only setting the drop effect.
        'Otherwise you will see no drop cursor, instead of Copy
        If (e.Data.GetDataPresent(DataFormats.FileDrop)) Then
            e.Effect = DragDropEffects.Copy
        Else
            e.Effect = DragDropEffects.None
        End If

    End Sub

    Private Sub txtEditor_DragDrop(ByVal sender As System.Object, _
                                   ByVal e As System.Windows.Forms.DragEventArgs) _
                                   Handles txtEditor.DragDrop
        'Getting the filename.
        'The length of files array will be based on the number of files dragging.
        Dim files As String() = e.Data.GetData(DataFormats.FileDrop)
        'Checking the files(0) is Sql File.
        If Path.GetExtension(files(0)).Equals(".sql", _
                                              StringComparison.CurrentCultureIgnoreCase) Then
            'Reading it using Stream reader
            Me.Text = String.Format("Drag Drop demo - {0}", _
                                    Path.GetFileNameWithoutExtension(files(0)))
            Using sr As New StreamReader(files(0))
                Me.txtEditor.Text = sr.ReadToEnd
            End Using
        Else
            'Otherwise displaying message box
            MessageBox.Show("Only supports SQL files")
        End If
    End Sub
End Class

Here is the screen shot

Drag and Drop Demo - Screenshot

If some one know a better implementation please let me know.

More details from MSDN :Performing Drag-and-Drop Operations in Windows Forms