The fairy tale was probably intended as a lesson to little girls not to talk to strange men, those metaphorical wolves who would prey on unsuspecting young women. A Freudian analysis--particularly given the importance of the cross-dressing male wolf, the bed (see image at right), and the young girl's scarlet cape--is fairly easy to perform here.
There are numerous versions of the story, some in which the wolf merely borrows Grandma's bonnet while she's out until Grandma returns and chases the wolf out, some where the story simply ends after the wolf gobbles Little Red Riding Hood up, and some that have both Grandma and Little Red Riding Hood swallowed whole by the wolf until they are saved by a huntsman who cuts them out of its belly.
The latter ending, found here in the Grimms' version, is rendered in delightfully gruesome detail: the wolf is vivisected and his belly filled with heavy stones until he collapses in death and the huntsman uses his pelt as a cloak. There is even a little coda about another wolf who tried to go after our crimson-capped heroine, and he is ultimately drowned in a trough of sausage-water (again, quite Freudian).
The sole consistency among all the story versions is that Little Red Riding Hood comments on what big body parts the wolf has. Unfortunately, this aspect of the tale does not fit with my Freudian reading. Hmm.
Grimm, Jacob and Wilhelm. "Little Red Cap." Nursery and Household Tales [Kinder- und Hausmärchen]. Berlin, 1812.