[This question is inspired by an astute observation from a student of mine.]
When we discuss conservation of momentum, students often ask, "When is momentum conserved?" And the lazy, mechanical response is often, "Momentum is always conserved."
A thoughtful student might then reply, "But what about falling objects? If I drop my pen, it accelerates towards the ground and gains momentum. Clearly, momentum is not always conserved."
This is a fair criticism. But one with an easy answer: "You aren't taking into account the momentum of the earth," we say, "As the earth pulls down on the pen, the pen (by Newton's Third Law) pulls up on the earth, accelerating it. Therefore, the downward momentum of the pen is cancelled out by the upward momentum of the earth.
"The more correct statement," we conclude, "is that momentum is always conserved in a closed system - namely, in a system containing all of the equal-and-opposite force pairs. None of the forces are allowed to cross the boundary of the system (like the weight of the pen does when you watch it fall without considering the earth)."
"Alright," the student concedes, "I'll buy that. But even when we neglect gravity, why doesn't momentum always appear to be conserved?"
"How do you mean?"
"I mean this: imagine floating in empty space - just you and a baseball. You look around and notice that you have zero momentum. And why shouldn't you? After all, you are in your own center of mass reference frame (where momentum is always zero).
"But then you throw the baseball," the student continues, "and it begins to move away from you with some momentum. However, from your point of view, you still are not moving. The system of you and the baseball is closed (there are no external forces), so momentum should be conserved. Yet before you threw the ball, momentum was zero, and afterwards, it is non-zero.
"What happened? Why was the momentum of this closed system not conserved?"