C++ templates Turing-complete?

I'm told that the template system in C++ is Turing-complete at compile time. This is mentioned in this post and also on wikipedia.

Can you provide a nontrivial example of a computation that exploits this property?

Is this fact useful in practice?

Example

#include <iostream>

template <int N> struct Factorial
{
    enum { val = Factorial<N-1>::val * N };
};

template<>
struct Factorial<0>
{
    enum { val = 1 };
};

int main()
{
    // Note this value is generated at compile time.
    // Also note that most compilers have a limit on the depth of the recursion available.
    std::cout << Factorial<4>::val << "\n";
}

That was a little fun but not very practical.

To answer the second part of the question:
Is this fact useful in practice?

Short Answer: Sort of.

Long Answer: Yes, but only if you are a template daemon.

To turn out good programming using template meta-programming that is really useful for others to use (ie a library) is really really tough (though do-able). To Help boost even has MPL aka (Meta Programming Library). But try debugging a compiler error in your template code and you will be in for a long hard ride.

But a good practical example of it being used for something useful:

Scott Meyers has been working extensions to the C++ language (I use the term loosely) using the templating facilities. You can read about his work here 'Enforcing Code Features'