Thanks - I was struggling to remember where I had heard of a practical application of the Fibonacci sequence in CS. The Fibonacci Heap was it - I'm pretty sure it was mentioned on my CS course and it must have been '87, same year it was published!
It seems like I had to as part of an interview once. Still, I have needed to write recursive functions many, many times and it's good to review some of what can go wrong.
[Edit:] But there are some interesting data structures based on them: http://en.wikipedia.org/wiki/Fibonacci_heap