Does AC current produce EM waves? Does AC current in simple wires produce electromagnetic waves? AC current entails very rapid changes in polarity and therefore the electrons in the metal will feel rapidly changing forces which should make them accelerate before attaining a constant drift velocity. Will this rapidly changing accelerations produce any electromagnetic wave, since the acceleration should be sinusoidal if the voltage source is, and hence the emitted electromagnetic wave should also be sinusoidal? Am I correct? If yes, why do we not account for energy lossd through EM waves in simple AC circuit analysis?
 A: You are right, the transmission of AC does in fact produce EM waves around it. These waves are indeed sinusoidal, but we do not bother about the power losses until we start sending radio signals via these wires because, until the frequency is much higher than radio waves, the energy lost is extremely small and hence negligible. See 

Ordinary electrical cables suffice to carry low frequency AC, such as mains power, which reverses direction 50 to 60 times per second. However, they cannot be used to carry currents in the radio frequency range or higher, which reverse direction millions to billions of times per second, because the energy tends to radiate off the cable as radio waves, causing power losses.
  (SOURCE : http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Transmission_line.html)

Even for radio signals we do not lose a lot of energy but it start making a significant effect thereafter, this is why we do not consider the losses encountered as EM wave transmission while handling single/low frequency AC circuits.
A: I think the issue is that while a powerline does produce fluctuating EM fields, that is not the same as EM "waves" or radiation. This distinction is summarized on  the wikipedia page about near vs far fields. In short, the two wires on a powerline have opposite phase, so that two adjacent pieces form an oscillating dipole, and we'd expect dipole radiation to escape from the powerline. However, the all these dipoles interfere with one another (because they are out of phase) and so the field that escapes to infinity is very small.
On the other hand, powerlines induce currents in the ground and nearby water, and this is a source of major losses. This is one reason powerlines are rarely buried, other than cost. Also, undersea power lines are often DC for this reason.
A: Actually alternating current is also an electromagnetic wave. The electrons in the ACcurrent travel on the conductor in a rotational movement. So the magnetic field created in the conductor also is rotational.
50/60 hz means the electrons rotates the conductor 50 or 60 times per seconds. It is not reversing the direction. Normally people think frequency means reversing the direction. Nope it rotates the conductor 50 or 60 times per second. So it is an EM wave. The frequency is low so the loss is high due to resistance in the conductor.
A: Yesterday I accidentally shortcircuited two wires (meant to enlighten a lightbulb) connected to a $50(Hz)$ AC current supply (with a mean value of $220(V)$). There were a flash and a little bang after which the fuse let a knob pop out. This is, of course, pathological behavior and the flash of light isn't provided by oscillating electrons, but by heating up the wire in a very short time (the same effect can appear, as might be clear, in a wire connected to a DC current supply, if the conditions are right), caused by collisions of electrons with the constituents of the wire. So, in an indirect way, EM radiation (coming from both the constituents and electrons, though the exact percentages of both I'm not sure of) can be produced in both AC as DC currents in simple wires, and must surely be taken into account in electrical circuits, for letting this pathological behavior not to happen.
