Consider deleting a node from a binary tree. You want a function that looks at a node and, if it's a match, unlinks it from its parent. Passing by reference allows you to do this cleanly. The alternative is to peek ahead at each subnode (messy) or to pass information up the call stack (inefficient, as the function can no longer be tail-recursive).
I'm not advocating C++ references, which I think are too implicit. If a function call foo(x) can change the value of x, there needs to be some visual indication of this. I'd prefer something like plain C pointers, with which you can pass the address of an object: foo(&x).
Of course an alternative is store objects wrapped in containers, and this isn't too bad a solution.
