Verne's novels were described by his publisher as "Les voyages extraordinaires" -- and this film, whatever licenses have been taken with the source, aspires to that. While the prelude to the journey is too long (we even have to endure Pat Boone croon a tuneless number), once we've plunged into the Earth, the film takes on an air of wonderment.
While the special effects are often praised, I think much of the wonder and awe of the film comes from the elaborate sets. And credit should also go to the music of Bernard Herrmann -- I doubt that had a better vehicle for his mystical, sonorous music.
Cast chemistry contributes in a big way. James Mason, a brooding but stout leader. Pat Boone, surprisingly effective as an eager student (but not so successful as a Scotsman). Arlene Dahl, a ravishingly beautiful damsel who is sage and sane and only distressed when she really really needs to be. Real-life Icelander Peter Ronson, a tall man's man -- who loves his pet duck. Gravelly-voiced Thayer David, pure villainy.
Add the final ingredient: a script that mixes fun and excitement with the fantastical.
The result is an extraordinary voyage for the teenager in you.