I doubt anybody teaches Euclid's Elements anymore, which is a shame. Many years ago, early in my high school days, I had to take a Geometry class. It seemed fairly useless at the time, but it was fascinating none the less. I spent hours with my compass and straight edge working from one proof to the next.
Upon reflection it turned out not to be useless at all. It was the first time I was exposed to a rigorous method of stepping from proof to proof to build a logical structure. In short, in its own abstract way, it did a wonderful job of teaching critical thinking. I wonder if today's school exercises on that skill do anywhere near as good a job?
I found a website dedicated to Euclid's Elements. It has all of his books in HTML form, as well as a java applet that provides you with a digital compass and straight edge. So, if out of either curiosity, nostalgia or geometric masochism you have a notion to fiddle with the proofs -- have at it.