Fans of The Jungle Book should be encouraged to read it's follow-up, The Second Jungle Book. The Second Book, much like it's predecessor, is a collection of animal themed short stories, and includes five additional stories about Mowgli.
Kipling's Just-So-Stories are another collection of animal-themed stories that are primarily written for young readers.
The Jungle Book (or at least the Mowgli portions) is often compared to the Tarzan books by Edgar Rice Burroughs. Both stories feature a feral child raised by animals, and both are highly familiar figures to modern people, largely do to their (frequently distorted) representations in film and other media.