There can be a few different contexts here to note(though I'm sure this has been mentioned over and over again):
1) If we are talking about a website having to give an "Oops, something bad happened," message then there should be simple language to tell the user that an error occured, please try again and if there are still issues to contact support at blah blah blah...
2) If we are talking about logging an exception thrown in code for sys admins and developers to read then the matter becomes more of taking the exception's message and stack trace to be recorded in either a log file, an e-mail, or the event viewer so that it can be handled differently depending on how urgent is it that someone looks into this.
3) If we are talking about writing the message for an exception then my suggestion is to clearly note what kind of error condition was met, e.g. is there a null reference where there shouldn't be or is there something worse like a file that should exist is missing, along with the severity of the error, e.g. can the application keep running or should it exit to an error page in this condition.