Metaphor, Analogy, or Simile

What is the appropriate use of these commonly mixed up words? Let's compare.

Metaphor: a figure of speech that uses a image, story, or tangible thing to represent another thing or some intangible quality or idea. For example, "All the world's a stage." -Shakespeare

Simile: compares two different things to create a new meaning. Often uses the words "like" or "as". For example, the world is like a stage.

Analogy: a comparison between two things that might seem different. Often used in standardized tests in the form "A is to B as C is to D".

Thanks Yahoo Answers