It is natural and common to produce test cases for as many acceptable input scenarios as possible. What is equally important -- but also uncommon -- is to produce an extensive set of test cases for all invalid or unexpected input.
For a simple example, let us say we are writing a program to sort lists of integers in the range of 0 to 100. Test lists should include some negative numbers, some nonintegral numbers, some alphabetic data, some null entries, and so on.
Reference:
Myers, G., The Art of Software Testing, New York: John Wiley & Sons, 1979.
