The energy of electromagnetic radiation is related to frequency; higher the frequency, higher the energy level. If electromagnetic waves have lower frequency when they arrive on Earth than originally emitted due to the Doppler effect, where, according to the conservation of energy, does the excess energy go?
It's spread out in time. If a source emits a 1W pule of energy lasting 1 second and the receiver is receding so fast that it is Doppler shifted to a frequency which means the power is just 0.5W, then the pulse will take 2seconds to arrive (since the end of it had further to travel).
Completely ignoring relativistic effects, it depends on which reference frame you are using; the "missing" energy is seen as kinetic energy in either the emitting or receiving atom as recoil depending on which one you view as moving. Energy is not conserved between reference frames.
If I am travelling at a velocity away from you, and I emit a photon at you which I observe to have a frequency f, then I will assume that photon has an energy E = hf, where h is the Planck constant. I will never observe a different energy for that photon - in my reference frame, energy is conserved. You, however, will observe a different frequency f, and therefore a different energy E. This energy remains constant for you - energy is conserved in your reference frame - but the energy I observe and the energy you observe differ - energy is not conserved between our reference frames; that is to say, the energy is conserved but not invariant
Consider - I drive past stationary you in a car and throw a tennis ball at you. In my perspective, the tennis ball has greater kinetic energy (it is moving at my speed, plus the speed of the ball) than in your perspective. Energy is not invariant in this circumstance either!
Conservation of energy doesn't apply to this situation because the energy you measure when at rest with respect to the source and the energy you measure when moving with respect to the source are in different reference frames. Energy is not conserved between different reference frames; in other words, if you're going to use conservation of energy, you have to make all your measurements without changing velocity.
For more information, have a look at https://physics.stackexchange.com/questions/1368/is-kinetic-energy-a-relative-quantity-will-it-make-inconsistent-equations-when-a.
varbatim from David Z's answer for a question on physics SE