In many database design tutorials/articles, they always bring up the fact that if two tables share a many-to-many relationship, then a third table should be created to act as an
Wikipedia describes it too. Just take a look: http://en.wikipedia.org/wiki/Many-to-many_(data_model)
If you still don't believe that many-to-many do realy need a third table, just try the Authors/Books examble (as described in the wikipedia article) with only two normalized tables.