One point not pointed out yet, is the speed. I know it's an old answered question, but I think this deserves direct comment/answer:
They would seem to be redundant as the same can be done with derived tables
When I used CTE the very first time I was absolutely stunned by it's speed. It was a case like from a textbook, very suitable for CTE, but in all ocurences I ever used CTE, there was a significant speed gain. My first query was complex with derived tables, taking long minutes to execute. With CTE it took fractions of seconds and left me shocked, that it is even possible.