private void Form1_Load(object sender,EventArgs e)
{
  DataGridView dgv = dataGridView1;
  dgv.Columns.Add("Spalte1","Spalte1");
  dgv.Columns.Add("Spalte2","Spalte2");
  dgv.Rows.Add(5); int i=0;
  foreach (DataGridViewRow dr in dgv.Rows)
    foreach (DataGridViewCell dc in dr.Cells) dc.Value = i++;
}

private Rectangle dragBoxFromMouseDown;
private int rowIndexFromMouseDown;
private int rowIndexOfItemUnderMouseToDrop;
private void dataGridView1_MouseMove(object sender,MouseEventArgs e)
{
  if ((e.Button & MouseButtons.Left) == MouseButtons.Left)
  {
    // If the mouse moves outside the rectangle, start the drag.
    if (dragBoxFromMouseDown != Rectangle.Empty &&
        !dragBoxFromMouseDown.Contains(e.X,e.Y))
    {
      // Proceed with the drag and drop, passing in the list item. 
      DragDropEffects dropEffect = dataGridView1.DoDragDrop(
        dataGridView1.Rows[rowIndexFromMouseDown],DragDropEffects.Move);
    }
  }
}

private void dataGridView1_MouseDown(object sender,MouseEventArgs e)
{
  // Get the index of the item the mouse is below.
  rowIndexFromMouseDown = dataGridView1.HitTest(e.X,e.Y).RowIndex;

  if (rowIndexFromMouseDown != -1)
  {
    // Remember the point where the mouse down occurred. 
    // The DragSize indicates the size that the mouse can move 
    // before a drag event should be started. 
    Size dragSize = SystemInformation.DragSize;

    // Create a rectangle using the DragSize, with the mouse position being
    // at the center of the rectangle.
    dragBoxFromMouseDown = new Rectangle(
      new Point(e.X - (dragSize.Width / 2),e.Y - (dragSize.Height / 2)),dragSize);
  }
  else
    // Reset the rectangle if the mouse is not over an item in the ListBox.
    dragBoxFromMouseDown = Rectangle.Empty;
}

private void dataGridView1_DragDrop(object sender,DragEventArgs e)
{
  // The mouse locations are relative to the screen, so they must be 
  // converted to client coordinates.
  Point clientPoint = dataGridView1.PointToClient(new Point(e.X,e.Y));

  // Get the row index of the item the mouse is below. 
  rowIndexOfItemUnderMouseToDrop =
    dataGridView1.HitTest(clientPoint.X,clientPoint.Y).RowIndex;

  // If the drag operation was a move then remove and insert the row.
  if (e.Effect == DragDropEffects.Move)
  {
    DataGridViewRow rowToMove = e.Data.GetData(
      typeof(DataGridViewRow)) as DataGridViewRow;
    dataGridView1.Rows.RemoveAt(rowIndexFromMouseDown);
    dataGridView1.Rows.Insert(rowIndexOfItemUnderMouseToDrop,rowToMove);
  }
}

private void dataGridView1_DragOver(object sender,DragEventArgs e)
{
  e.Effect = DragDropEffects.Move;
}