I think sorting methods are a very good example of what an algorithm is. But it only becomes a good example when you compare various methods. If you can only teach one, I'm not sure it's worthwhile.
Realisticly, we call the sort method in some framework. So if you can't effectively teach about the sorting alorithms, it might not be worth the time.
Nobody has to write a sort method anymore, but it's still a very good example of the impact of algorithms.
