What DKII said.. Jumping puzzles and obstacle avoidance are the core atoms of a platformer.
Donkey Kong and Mario Bros. were both pure platformers.
Later Mario games weren't quite as pure, though they retained the FOCUS on jumping puzzles and that tends to be what decides the genre of the game.
I don't consider Ratchet & Clank Future a platformer, for instance. It's actually a run-n-gun, with pretty much equal focus on the shooting and platforming elements.







