type
  TForm1 = class(TForm)
    StringGrid1: TStringGrid;
    ListBox1: TListBox;
    procedure ListBox1DragOver(Sender, Source: TObject; X, Y: Integer;
      State: TDragState; var Accept: Boolean);
    procedure ListBox1DragDrop(Sender, Source: TObject; X, Y: Integer);
    procedure FormCreate(Sender: TObject);
    procedure StringGrid1DragOver(Sender, Source: TObject; X, Y: Integer;
      State: TDragState; var Accept: Boolean);
    procedure StringGrid1DragDrop(Sender, Source: TObject; X, Y: Integer);
  private
    { Private declarations }
    XMouseCord: Integer;
    StartDrag: Boolean;
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.DFM}

procedure TForm1.ListBox1DragOver(Sender, Source: TObject; X, Y: Integer;
  State: TDragState; var Accept: Boolean);
begin
  Accept := Source is TStringGrid;
end;

procedure TForm1.ListBox1DragDrop(Sender, Source: TObject; X, Y: Integer);
var
  i: integer;
  ColumVal, CurrentCol: Integer;
begin
  if Source is TStringGrid then
  begin
    //Вычисляем колонку
    ColumVal := 0;
    CurrentCol := 0;
    for i := 0 to TStringGrid(Source).ColCount - 1 do
    begin
      ColumVal := ColumVal + TStringGrid(Source).ColWidths[i];
      if XMouseCord <= ColumVal then
      begin
        CurrentCol := i;
        break;
      end;
    end;
    //Убеждаемся, что это не первая колонка, которая не содержит данных
    if CurrentCol <> 0 then
    begin
      for i := 1 to TStringGrid(Source).RowCount - 1 do
      begin
        ListBox1.items.Add(TStringGrid(Source).Cells[CurrentCol, i]);
      end;
    end;
    StartDrag := True;
  end;
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
//Для демонстрационных целей
  with StringGrid1 do
  begin
    Cells[1, 1] := 'T1';
    Cells[1, 2] := 'T2';
    Cells[1, 3] := 'T3';
    Cells[1, 4] := 'T4';
    Cells[2, 1] := 'T5';
    Cells[2, 2] := 'T6';
    Cells[2, 3] := 'T7';
    Cells[2, 4] := 'T8';
    Cells[3, 1] := 'T9';
    Cells[3, 2] := 'T10';
    Cells[3, 3] := 'T11';
    Cells[3, 4] := 'T12';
    Cells[4, 1] := 'T13';
    Cells[4, 2] := 'T14';
    Cells[4, 3] := 'T15';
    Cells[4, 4] := 'T16';
  end;
  StartDrag := True;
end;

procedure TForm1.StringGrid1DragOver(Sender, Source: TObject; X,
  Y: Integer; State: TDragState; var Accept: Boolean);
begin
  //Сохраняем колонку, когда начинается перетаскивание.
  if StartDrag then
  begin
    XMouseCord := X;
    StartDrag := False;
  end;
end;

procedure TForm1.StringGrid1DragDrop(Sender, Source: TObject; X,
  Y: Integer);
begin
  //В данном случае помещаем е¸ на грид
  StartDrag := True;
end;