[roman]

Código Delphi [-]
procedure DirList(Path: String; List: TStrings);
var
  SearchRec: TSearchRec;

begin
  Path := IncludeTrailingPathDelimiter(Path);

  if FindFirst(Path + '*.*', faAnyFile, SearchRec) = 0 then
  begin
    List.BeginUpdate;

    repeat
      if (SearchRec.Name <> '.') and (SearchRec.Name <> '..') then
      begin
        if (SearchRec.Attr and faDirectory = faDirectory) then
        begin
          List.Add(Path + SearchRec.Name + '\');
          DirList(Path + SearchRec.Name, List);
        end
        else
          List.Add(Path + SearchRec.Name);
      end;
    until FindNext(SearchRec) <> 0;

    List.EndUpdate;
  end;

  FindClose(SearchRec);
end;

Código Delphi [-]
// Uso
DirList('C:\Mis documentos', ListBox1.Items);

No es la forma óptima y si lo ejecutas contra 'C:\' prepárate a esperar un buen rato.

// Saludos