c++ - Best way to keep track of game objects

I'm not exactly sure how I should ask this question, and so the title may be misleading - I am not asking if I should use a list or a stack or a vector or a queue - but how I should go about keeping track of said storage object.

For example, let's say I have some object that would represent the game itself, and the game used state objects to tell what state it was in(IE, playing, paused, titlescreen, gameover screen, etc etc):

class Game
{
    //Constructors and what not
    private: 
    stack states;

};

And then each state would keep track of the objects that it contained.

class States
{
    //Constructors and whatnot
    private:
    list listOfMobs;
    list listOfBullets;
};

Now, what if I have a Mob spawn new Mobs, or have a Mob fire a bullet? I definitely don't want to pass the State itself down to all Mobs - I'd have dozens(or more) of copies of the State wandering around, which does not seem very wise. In the same sense, passing down the list of Mobs or bullets does not seem like the best idea either. So, how should I handle this? I don't want to use global variables, and in the same way I wouldn't like to use a singleton pattern to keep track of it all - but I don't see very many other options. I might just be stuck thinking inside the proverbial box, though. How does everyone else handle tracking the objects in their game?