Оформил: DeeCo
Автор: http://www.swissdelphicenter.ch

function AppendOrWriteTextToFile(FileName : TFilename; WriteText : string): boolean;
 var
   f : Textfile;
 begin
   Result := False;
   AssignFile(f, FileName);
   try
     if FileExists(FileName) = False then
       Rewrite(f)
     else
     begin
       Append(f);
     end;
     Writeln(f, WriteText);
     Result := True;
   finally
     CloseFile(f);
   end;
 end;

 // Sample Source... 
procedure TForm1.Close1Click(Sender : TObject);
 var
   dir, log : string;
 begin
   dir := ExtractFilePath(Application.Exename);
   log := 'Last Programm Termination: ' + DateTimeToStr(now);
   AppendOrWriteTextToFile(dir + '\logfile.txt', log)
 end;