There is no (buggy) character controlled like in other engines, you need to program your own (buggy) character controller (like one usually ends doing in other engines xD).
That said, there is an API on KinematicBody (move) that is useful for p/np controlled characters.
You can see an implementation of it on the Kinematic Character demo.
In Godot 3,
move_and_slide makes programming controlled characters easier without compromising flexibility (demo on master branch uses this).
RigidBody also have a Character mode, which nulls rotations and also the possibility to use a "custom integrator" to modify the body state (velocities) used by the physics engine.
The 3D platformer demo is an example of this type of bodies.
ps: Up to Godot 2.1.x, KinematicBody is limited to the use only of layers to detect collisions, RigidBody use masks instead (which is the "correct" way).