Squash and Stretch:
Squashing and stretching an object or character in animation helps give the illusion of weight and mass, aiding a lot in movement and facial animations.
Anticipation:
This is the anticipation of an action. For example, for a punch, a character would have a build-up of twisting their body and pulling back their torso and arm before the major action. This principle applies to all movements in animation.

Staging:
This pertains to the animation scene as a whole. Cameras must be well-placed to achieve a certain effect, characters must be clear in their expressions so as not to confuse the viewer, the background should not be competing for attention with the foreground elements, etc.

Straight Ahead and Pose-to-Pose Animation:
These are two very different ways of animating. 'Straight Ahead' means that the animator will first draw the beginning of a sequence and will work to the end of the scene straight from there which can result in some mistakes but has a spontaneity that 'pose-to-pose' doesn't. Whereas 'Pose-to-Pose' is when a lead animator will draw key frames throughout a sequence and then sending it off to someone else to fill in the blanks. This results in a much more neat and controlled animation.

Follow-Through and Overlapping Action:
Both of these refer to the continued movement of things attached to the main body of a character after movement or a change of direction. 'Follow-through' is the continued movement of hair, limbs, and clothing once a character has fully come to a stop whereas 'overlapping action' is when these same things continue moving in the original direction for a short while after a character suddenly changes direction.

Slow-Out and Slow-In:
This is the use of more frames of animation before and after an action. This causes action to seem to slower at the beginning and end, resulting in something far more realistic and believable.

Arcs:
The majority of animated characters and objects (with robotics and machinery being an exception) follow a curve as opposed to a straight, direct line.

Secondary Action:
An action used to compliment another, reinforcing a certain feeling or emotion in a character.

Timing:
The use of frames as a means to determine how long an action will be on-screen and how fast the particular animation should last.

Exaggeration:
This is a technique commonly used in very cartoony animations. It takes a movement and greatly exaggerates every part of it to make it clearer for the viewer as well as giving the sequence more appeal.

Solid Drawing:
The principle of creating weight, form and a sense of a third dimension within a 2D drawing.

Appeal:
It doesn't matter if a character is good or evil, it has to have some kind of appeal to help capture the audiences interest.