Inner Vs. Outer Join

What is the difference between and inner and out join in SQL?  I hear this question a lot (at work, when I conduct interviews, and when I'm interviewed).  The answer isn't as straight forward as you may think.  Here is a diagram from the article  "Visual Representation of SQL Joins" by C.L. Moffat that show's a visual representation of what each time of join does:

There are other good discussion on the difference between inner and outer joins found in Stack Overflow.