Maybe think the movie "War Games"?
OverTheWire WargamesThe wargames offered by the OverTheWire community can help you to learn and practice security concepts in the form of fun-filled games.
Yes, you ssh into someone's host and learn security and hacking concepts in a game-like fashion.
There's a goodly number of these kinds of things:
We Chall For the people not familiar with challenge sites, a challenge site is mainly a site focused on offering computer-related problems. Users can register at such a site and start solving challenges. There exist lots of different challenge types. The most common ones are the following: Cryptographic, Crackit, Steganography, Programming, Logic and Math/Science. The difficulty of these challenges vary as well.