I once caught a student plagiarizing when I noticed that her writing had suddenly become, well, coherent and just plain grammatical. When I called her into my office and confronted her, she cried and insisted that she didn't mean to cheat (It must have been an accident!) and that she didn't knowingly copy whole strings of phrases from her book. I did show a bit of mercy and didn't levy the maximum penalty, and in a final bit of justice she ended up failing the course anyway.
But the best part of the story comes after I confronted her. About fifteen minutes after she left my office, I got an e-mail from the Dean of Students informing me that she was complaining because I implicitly questioned her integrity! I couldn't believe it! I thought I had questioned her integrity in no uncertain terms.
And just for some perspective, I would like to say that I have been pleasantly surprised by my students over the last three years. While maybe one in thirty of my students gets caught cheating (I'm sure more do it, but that's still a very low figure), the majority of men and women who come through my classes have responded very well to the challenges I try to build into my syllabi.