Intrusive containers can be used for highly optimized algorithms, where speed is a crucial issue and:

The last point is important if you have a lot of containers over a set of elements. E.g. if you have a vector of objects (say, std::vector<Object>), and you also have a list storing a subset of those objects (std::list<Object*>), then operating on an Object from the list iterator (std::list<Object*>::iterator) requires two steps:

While the objects themselves are tightly packed in the memory of the vector (a vector's memory is guaranteed to be contiguous), and form something like a data block, list nodes may be dispersed in the heap memory. Hence depending on your system you might get a lot of cache misses. The same doesn't hold for an intrusive list. Indeed, dereferencing an iterator from an intrusive list is performed in the same two steps as described above. But the list node is already embedded in the Object, so the memory is directly tracked from the iterator to the Object.

It's also possible to use intrusive containers when the objects to be stored can have different or unknown size. This allows storing base and derived objects in the same container, as shown in the following example:

#include <boost/intrusive/list.hpp>

using namespace boost::intrusive;

//An abstract class that can be inserted in an intrusive list
class Window : public list_base_hook<>
{
   public:
   //This is a container those value is an abstract class: you can't do this with std::list.
   typedef list<Window> win_list;

   //A static intrusive list declaration
   static win_list all_windows;

   //Constructor. Includes this window in the list
   Window()             {  all_windows.push_back(*this);  }
   //Destructor. Removes this node from the list
   virtual ~Window()    {  all_windows.erase(win_list::s_iterator_to(*this));  }
   //Pure virtual function to be implemented by derived classes
   virtual void Paint() = 0;
};

//The static intrusive list declaration
Window::win_list Window::all_windows;

//Some Window derived classes
class FrameWindow :  public Window
{  virtual void Paint() BOOST_OVERRIDE {/**/} };

class EditWindow :  public Window
{  virtual void Paint() BOOST_OVERRIDE {/**/} };

class CanvasWindow :  public Window
{  virtual void Paint() BOOST_OVERRIDE {/**/} };

//A function that prints all windows stored in the intrusive list
void paint_all_windows()
{
   for(Window::win_list::iterator i(Window::all_windows.begin())
                                , e(Window::all_windows.end())
      ; i != e; ++i)
      i->Paint();
}

//...

//A class derived from Window
class MainWindow  :  public Window
{
   FrameWindow   frame_;  //these are derived from Window too
   EditWindow    edit_;
   CanvasWindow  canvas_;

   public:
   void Paint() BOOST_OVERRIDE {/**/}
   //...
};

//Main function
int main()
{
   //When a Window class is created, is automatically registered in the global list
   MainWindow window;

   //Paint all the windows, sub-windows and so on
   paint_all_windows();

   //All the windows are automatically unregistered in their destructors.
   return 0;
}

Due to certain properties of intrusive containers they are often more difficult to use than their STL-counterparts. That's why you should avoid them in public interfaces of libraries. Classes to be stored in intrusive containers must change their implementation to store the hook and this is not always possible or desirable.