I’m guessing you’ve already read the Black Swan (or at least a decent précis). You already know that most financial data do not follow normal distributions. For example stock prices are not normally distributed. They’re not log-normally distributed either. In fact we don’t have a distribution that can be used to model stock prices! But we still pretend they are. Option are still prices using Black-Sholes and we’ll stick the normal distribution in there, because it’s easy to do.
Here’s something else that isn’t normal, but is often treated as being normally distributed. Employee performance. If you are a software engineer you already know this to be true. The best programmers are easily 10’s of times better than the next best. They can churn out more useful stuff in a week than most ordinary folk can in a year. And yet, we grade them on a normal scale. Ever worked for a bank? For GE (spit, spit)? Well you know what I mean. The forced A,B,C grading. The assumption that 80% of the people deserve ‘B’s and that 10% deserve ‘A’s and so on.
Anyways, rants aside, here’s a very interesting look at human achievement: http://www.johndcook.com/blog/2009/09/29/achievement-is-log-normal/. Its an interesting read just for the statistics. And probably one of the better explanations of what a log-normal distribution is.