How does a fixed amount of transmitted radio energy supply an unknown number of destinations? I did some maths and physics up to the age of 18, and hold an amateur radio licence. This thing has puzzled me for a while - does reception of an electromagnetic wave imply an interaction with the transmitter? Does it drain some of the transmitter's energy?
 A: A wavefront (your signal) has a fixed amount of energy given to it by the transmitter.  Whatever happens to the wave once it leaves the transmitter is independent of the transmitter, thus receiving a signal does not drain any additional energy from the transmitter (though it can drain energy from the wavefront itself).
EDIT:  As pointed out by @Alfred Centauri in the comments, the transmitter would be affected if the receiver was in the near field.  For amateur radio purposes, the near field ceases to exist well within 200 meters of the transmitter (for the vast majority of cases), thus it is unlikely that anyone "tuning in" to your broadcast would be directly affecting your transmitter.
A: The confusion you face is a historical one.  Originally the interactions of different bodies was thought to happen at a distance more or less instantly, such as the case in the time of Newton and his gravitational theory.
But when we discovered electromagnetism, and in particular, when Maxwell completed his formulation of Electromagnetism as contained in Maxwell's Equations, he re-expressed the laws of electromagnetism in a way that would change the future evolution of physics.
 It was actually Faraday that introduced the notion of "fields". But one could argue, if it were not for Maxwell's mathematical description, it would have been unlikely to have the impact it did as quickly as it did
$$ \mathbf \nabla \cdot \mathbf E = \frac{\rho}{\epsilon_0} \qquad \mathbf \nabla \times \mathbf E = -\frac{\partial B}{\partial t} $$
$$ \mathbf \nabla \cdot \mathbf B = 0 \qquad \mathbf \nabla \times \mathbf B = \mu_0 \left( \mathbf J + \epsilon_0 \frac{\partial E}{\partial t } \right) $$
The equations look scary, but the think I want to draw attention to is that these are fundamentally field equations, describing the evolution of the electric and magnetic fields themselves.  
Granted, these are completely equivalent to other descriptions of Electricity and Magnetism you might be more familiar with, for instance things like Coloumb's law:
$$ \mathbf F = \frac{ k q_1 q_2 }{ r^2 } \hat r $$
But the idea behind Maxwell's formulation is very different.  The electric and magnetic fields take center stage themselves, suddenly promoted to very real and tangible things that exist everywhere and follow their own set of laws.  At first, many contemporaries were deeply bothered by this.  Sure, they would say, the electric and magnetic fields are perfectly fine mathematical tricks you can use to solve problems easier, but they can't be real.
But, they are real, real in every sense of the word.  In particular, the discovery that would convert many minds is that the electric and magnetic fields store a quantifiable amount of energy.  In particular, the amount of energy stored in the electric and magnetic fields is proportional to the square of their magnitudes.
$$ \frac 12 \epsilon | \mathbf E |^2 \quad \text{ or } \quad  \frac {1}{2\mu} | \mathbf B |^2 $$
Suddenly it became very awkward to try to deny the existence of the electric and magnetic fields.  If you didn't want to assign any sort of ontological status to the fields themselves, you are suddenly in the position of having to come up with very long and convoluted excuses for why in some simple electric experiments it would appear as though the energy was not conserved.
Once this idea was fully embraced it would open the door to most of modern physics.  A large fraction of all physics these days tied to the study of field equations, be they in high energy physics, or plasmas, or fluids, or continuum material theories, etc.  
Returning to the question at hand.  Once you have embraced the idea that the electric and magnetic fields are real entities, I think the answer to your question becomes natural.  Your transmitter looses energy as soon as it tries to interact with the electric and magnetic fields at your antenna.  After that, the disturbances you have bought and paid for start propagating according to Maxwell's equations, for the most part just spreading out from your antenna.  Whether or not anyone listens in to your SSB or CW transmissions (Hams unite!) doesn't affect your transmitter.  Bought and paid for.  On the receiving end, they are actually converting the energy content of the electric and magnetic fields (at their own antenna) into the electric signals in their receiver, which when amplified and pumped through their headphones ensure 59s all around. 73.
