[c++11] When is std::weak_ptr useful?

I see std::weak_ptr<T> as a handle to a std::shared_ptr<T>: It allows me to get the std::shared_ptr<T> if it still exists, but it will not extend its lifetime. There are several scenarios when such point of view is useful:

// Some sort of image; very expensive to create.
std::shared_ptr< Texture > texture;

// A Widget should be able to quickly get a handle to a Texture. On the
// other hand, I don't want to keep Textures around just because a widget
// may need it.

struct Widget {
    std::weak_ptr< Texture > texture_handle;
    void render() {
        if (auto texture = texture_handle.get(); texture) {
            // do stuff with texture. Warning: `texture`
            // is now extending the lifetime because it
            // is a std::shared_ptr< Texture >.
        } else {
            // gracefully degrade; there's no texture.
        }
    }
};

Another important scenario is to break cycles in data structures.

// Asking for trouble because a node owns the next node, and the next node owns
// the previous node: memory leak; no destructors automatically called.
struct Node {
    std::shared_ptr< Node > next;
    std::shared_ptr< Node > prev;
};

// Asking for trouble because a parent owns its children and children own their
// parents: memory leak; no destructors automatically called.
struct Node {
    std::shared_ptr< Node > parent;
    std::shared_ptr< Node > left_child;
    std::shared_ptr< Node > right_child;
};

// Better: break dependencies using a std::weak_ptr (but not best way to do it;
// see Herb Sutter's talk).
struct Node {
    std::shared_ptr< Node > next;
    std::weak_ptr< Node > prev;
};

// Better: break dependencies using a std::weak_ptr (but not best way to do it;
// see Herb Sutter's talk).
struct Node {
    std::weak_ptr< Node > parent;
    std::shared_ptr< Node > left_child;
    std::shared_ptr< Node > right_child;
};

Herb Sutter has an excellent talk that explains the best use of language features (in this case smart pointers) to ensure Leak Freedom by Default (meaning: everything clicks in place by construction; you can hardly screw it up). It is a must watch.