Assertions are not evil but they can be easily misused. I do agree with the statement that "assertions are often used as a crutch to avoid thinking about proper error handling and reporting". I have seen this quite often.
Personally, I do like to use assertions because they document assumptions that I might have made whilst writing my code. If these assumptions are broken while maintaining the code, the problem can be detected during test. However, I do make the point of stripping out every assert from my code when doing a production build (i.e., using #ifdefs). By stripping out the assertions in the production build, I eliminate the risk of anyone misusing them as a crutch.
There is also another problem with assertions. Assertions are only checked at run-time. But it is often the case that the check you would like to perform could have been performed at compile-time. It is preferable to detect an issue at compile time. For C++ programmers, boost provides BOOST_STATIC_ASSERT which allows you to do this. For C programmers, this article ( link text ) describes a technique that can be used to perform assertions at compile time.
In summary, the rule of thumb I follow is: Do not use assertions in a production build and, if possible, only use assertions for things that cannot be verified at compile-time (i.e., must be checked at run-time).