uses
clipbrd;

private
procedure wmdrawclipboard(var message: tmessage); message wm_drawclipboard;
...

var
Form1: TForm1;
NextViewer: THandle;
implementation

{$R *.DFM}

procedure TForm1.wmdrawclipboard(var message: tmessage);
begin
if Clipboard.HasFormat(CF_TEXT) then Memo1.Text:=Clipboard.AsText;
end;

procedure TForm1.FormShow(Sender: TObject);
begin
NextViewer:=SetClipboardViewer(Handle);
end;

procedure TForm1.FormDestroy(Sender: TObject);
begin
ChangeClipboardChain(Handle, NextViewer);
end;