[Khronos]

Otra forma sería así:

Código Delphi [-]
program Project1;

uses
  Windows, Forms, Unit1 in 'Unit1.pas' {Form1};

{$R *.res}
var
  hMutex: THandle;
begin
  hMutex:= OpenMutex(MUTEX_ALL_ACCESS, false, pchar('APP'));
  If hMutex = 0 then
    begin
      CreateMutex(nil, true, pchar('APP'));
      WinExec(pchar(paramstr(0)), SW_SHOWNORMAL);
      ExitProcess(0);
    end;
  Application.Initialize;
  Application.CreateForm(TForm1, Form1);
  Application.Run;
end.

EDITO: Luego en el evento OnClose del Form principal pondríamos algo así: CloseHandle(hMutex);

Saludos.