E.T.'s popularity ensures it can get along quite nicely without critics analysing, interpreting and explaining why it works. It works because it touches that (uncritical, non-analytical) childlike part of us that we often need to be reminded is still there. It's the part that believes in the supreme power of love and has an innocent faith in magic. The part that urges us to clap so Tinker Bell may live.
The movie's emotional core is the relationship between a sensitive 10 year old boy named Elliot (Henry Thomas is achingly honest in this role) and an abandoned Extra-Terrestrial he finds in his garage. The story is told literally from a child's viewpoint, as the adults are filmed from belt-buckle height; consequently, we don't see the faces of many of the shadowy figures eavesdropping on Elliot's house. In typical Spielberg fashion, the children are the heroes, and most of the adults completely untrustworthy. This oversimplification of characters works here because the bond between Elliot and E.T. rivets us and adults want to tear them apart in the name of science and reason.
Elliot and E.T. develop a telepathic connection of sorts -- they share each other's feelings. The evolution of their relationship is sweet and touching, and eventually leads Elliot to realise that E.T. needs to go home. Earth is making him sick. The second half of the film follows this pursuit, and provides the action, laughter and tears that close the film.
Is E.T. a religious allegory, because it is the pure of heart, the innocent, those in pain, who E.T. reveals himself to first and who form a 'spiritual' connection with him? Is E.T.'s desire to go home a metaphor for resurrection? In the end, it doesn't really matter. What does matter is that E.T. reminds us why we still clap in Peter Pan. And Tinker Bell does live.