What has been discussed here, as far as energy being converted from one form to another, is definitely true. However, there is usually more to it than that. Consider a Jupiter probe from Earth that uses Venus as a "slingshot" to increase it's velocity. In the cases so far, it would gain kinetic energy while falling into the gravity well of Venus, and then loose it again as it climbed out. Since it has farther to climb out (all the way to Jupiter) than it had going in (from Earth), it seems hardly worth the effort for what would, at most, be a simple change in direction during the fly-by.
The point is that Venus has kinetic energy of it's own, in it's orbit around the sun. The trick is to rob it of some of that energy, adding it to the probe, and thus very much increasing it's velocity, while minusculely retarding Venus in its path. In this case we have an actual transfer of energy from one body to another. This transfer also obviously occurs if any of the bodies collide, whether elastically or inelastically (or anything in between).
Another possibility can be seen by examining the earth-moon system. The moon is slowly increasing its distance from earth, thereby increasing it's potential energy. Where is that energy coming from? It happens that the equatorial bulge that the Earth maintains accelerates the moon periodically, asymmetrically. Its costs the earth some small angular energy and momentum to do so. Eventually the moon will be much farther away and the earth's day will be slowed until it synchronizes with the moon. Another example of energy transfer - remember that rotating masses also have a form of kinetic energy in proportion to their angular velocity squared, as well as whatever linear energy they have.
I heard someone speak above about the energy being distributed within the system. That is true, in the sense that separating bodies increases the potential energy between them, but energy is also intimately tied to mass (or inertia, linear or rotational) and so it is quite proper to speak of a mass having kinetic energy and potential energy with respect to another mass. Without mass neither exists (that is, potential and kinetic cannot; chemical, acoustic, nuclear, hydraulic, radiational, etc, etc certainly still do). However, k & p energy can only be measured from some arbitrary platform, and only then can numbers be assigned of energies to the masses in the system.