1. Squash & Stretch

This is the most important principle. It gives an object a sense of weight and flexibility. Could be simple like a bouncing ball or more complex like a character being exaggerated for a comical effect. In realistic animation the object's volume does not change when squashed or stretched.

2. Anticipation

Anticipation is used to prepare the audience for a big movement and makes the action appear more realistic. The amount of anticipation is determined by the speed of the action following it.  If the movement is not very fast then the anticipation can be small.  If it’s a big movement then the anticipation needs to be more pronounced.

EXAMPLES
Have the animated object move in the opposite direction before it continues forward.

3. Ease In and Ease Out

The slow into & out of the animation.
When objects start their movement you need to give them time to accelerate and slow down. This creates a more appealing and realistic animation.  In motion graphics this can be utilized in just about everything you animate. Natural objects don't start moving at top speed. They always start slow then accelerate. Think about a car. It dosn't go from 0-100 miles per hour instantly. With out this your animations will appear very robotic. 

4. Timing

Timing refers to the speed of the action. Correct timing gives the illusion that the object obeys the laws of physics. It can also define the weight of objects. 

EXAMPLES
When animating a feather falling, you would want the timing to be spread out to give the feeling the object is almost weightless.

TEXT
Must have the right timing to give the viewer enough time to read the text comfortably. If you can read it fast 2-3 times that is good. If there's a voice over it can be faster.

CHARACTERS
Timing is critical for establishing a character's mood, emotion, and reaction. It can also be a device to communicate aspects of a character's personality.

5. Staging

The purpose is to direct the audience’s attention. What is has the greatest importance in a scene.  Make it completely and unmistakably clear. The essence of this principle is keeping focus on what is relevant, and avoiding unnecessary detail.

Staging is the presentation the idea. The placement of elements in the frame, the position of the camera, or even the lighting, camera angle or position of the camera.

What should the viewer be looking at?
This should be clear. If the staging is not right in your scene, the audience will have trouble focusing on whats important, or they might be focusing on the wrong element entirely. What Is the main point of this shot and what do you want to communicate to the viewer?

6. Arcs

Almost nothing moves linearly with the exception of mechanical movement, which typically moves in straight lines. Things like robots or machines.

To avoid motion graphics that don’t look robotic, you need to consider arcs in everything you do.

A great place to incorporate nice arcs into your motion design is during camera movements.
Smoother transition and is more pleasant for the viewer. Linear camera movement can feel jerky. Generally the faster the object the longer the arc.

EXAMPLES:
Rocket ship blasting into the air.
Bee buzzing across the screen.

7. Exaggeration

Exaggeration especially useful for animation. Perfectly imitating reality can look static and dull in cartoons. The level of exaggeration depends on the amount of realism in a particular style. Apply a level of restraint when using exaggeration. There should be a balance on how those elements are exaggerated in relation to each other to avoid confusing or overwhelming the viewer.

EXAMPLE
Alterations in the physical features or movements of a character.