Peter Donnelly talks about the misuse of statistics in his TED talk a couple of years back. The first 2/3 of the talk is an introduction to probability and its role in genetics, which admittedly, didn't get much of my interest. The last third, however, gets a lot more interesting.
Donnelly talks about a British woman who was wrongly convicted largely in part because of a misuse of statistics. A so-called expert cited how improbable it would be for two children to die of sudden infant death syndrome, but it turns out that "expert" was making incorrect assumptions about the data. This doesn't surprise me since it happens all the time.
People misuse statistics every day (intentionally and unintentionally), and oftentimes it doesn't hurt much (which doesn't make it any better), but in this case improper use directly affected someone's life in a very big way. One of the most common assumptions I see is that every observation is independent, which often is not the case. As a simple example, if it's raining today, does that change the probability that it will rain tomorrow? What it didn't rain today?
In other words, the next time you're thinking of making up or tweaking data, don't; and the next time you need to analyze some data but aren't sure how, ask for some help. Statisticians are nice and oh so awesome.
Here's Donnelly's talk: