Do radio waves travel around the Earth or through it? Whenever you hear someone illustrating/describing the transmission of radio waves they always make it seem like they'd travel perfectly around the Earth to another distant location. For example, a radio wave sent by alternating current to be received from an intercepting device on the other side of the planet. 
You'd think of something like:

Top frame shows how most media works, etc., would illustrate it: radio waves illustrated to go perfectly wrapped around Earth like a straight line until it gets to the other side.
Bottom frame shows how it should work (supposedly) if radio waves travel at all directions at the speed of light: will go right through the ground to the other side of the planet.
Basically, it will travel in all directions, but measuring how it gets there it should really appear like this, no?

To put the question in perspective, will radio waves go right through the ground and reach the other point near instantly, all on the other side of the Earth? 
 A: Amateur "ham" radio operators who communicate with HF (3.0 to 30 MHz) frequencies can hear their own signal as it has circumnavigated the globe.  This almost only happens with operators using Morse Code (CW) where the distinct signal can be heard and detected with sub-second intervals.
Also, ham operators make a distinction between short path (SP) and long path (LP) contacts.  Short path is basically the shorter portion of the line (geodesic) between two points and LP is the longer portion of the line.  Due to propagation changes such as due to the movement of the sun where the skip distance can change plus other effects that cause QSB (cyclic fading) some QSOs actually will use SP and LP at various times.  Oh, a QSO is a communication conversation.
These effects of SP and LP comms along with hearing your own signal are well documented and even performed via lab quality instrumentation.  It is though rare as the skip zones rob power from the signal so to do LP comms requires higher power (usually).
But, traveling through the Earth -- No.
A: No, radio signals do not go through the Earth. Not for any one reason, but for a series of reasons, many of which have been talked about here so I will make a comprehensive list, and there might be even more to add on!


*

*The Earth is quite dense: As @Renan pointed out, x-rays can't even penetrate bone, and the photons in an x-ray are significantly more energetic than the ones in radio waves (plus the Earth is much denser than the human body). 

*Atmosphere: The atmosphere in general will not keep signals inside the Earth, which is why we can communicate with satellites just fine. However, the waves coming off of a transmitter aren't really going in a straight line. This is only an approximation. In real life, most materials are dispersive so the light will move differently based on various aspects (check that link). If the conditions are just right, like the atmospheric region has the right water content, and the signal is sent at a certain frequency, one can get reflection from the atmosphere. This is called over the horizon (OTH) in the radar world. So now we have a signal travelling back down towards the Earth's surface. Will it penetrate? This is where it gets interesting.

*On the surface: one of three things can happen, (a) the wave is heading towards water, (b) the wave is heading towards land or (c) the wave is heading towards an object (on land or water). The third case will either reflect the wave straight back up (then off the atmosphere and back to the receiver, etc) or will eventually become case (a) or (b) so we will focus on those.


*

*(a): if the wave is heading towards water, this is simple. At most microwave (subset of radio) frequencies water acts like a mirror, completely reflecting the wave. This is exactly why submarines are completely invisible to radar and one must use sonar to track them. So no penetration.

*(b): if the wave is going towards the Earth's surface and it is not water, it is likely to be soil. Most soils have a high concentration of metals (often iron, sometimes magnesium). To the wave, these metals will resemble a perfect electrical conductor, just like the water. Although the ground may not be as smooth as the water so you would get some crazy scatter. But either way, no penetration.
Edit: I forgot to mention one important thing about antennas. You may or may not know this but antennas (transmitter or receiver) have a characteristic called directivity. Directivity is basically the measure of how focused a beam is. So in general, signals will be sent with specific "beam widths" to avoid hitting things that they don't want to hit. You're thinking of an isotropic monopole antenna, which radiates equally in all directions. However, isotropic monopoles cannot be fabricated, so pretty much every antenna that you see is very focused on sending the energy to a certain spot, with very little going the wrong way like to the ground or straight up.
A: The actual reason that radiowaves do not penetrate the Earth, which is that the Earth is partly or very conductive and either dissipates or reflects the waves.
The dissipation length or "skin depth" at most radio wave frequencies is a few to tens of metres at most.
However, this conductivity, especially seawater, combined with the conductivity in the ionosphere make an excellent waveguide (a bit like a fiber-optic cable) that allows radiowaves at certain frequencies to travel around the globe.
A: Radio waves will not travel through the Earth. It's just too dense for that.
Think of it this way: when you take an x-ray, you can see your skeleton in detail in the photograph. That's because when a beam of x-rays goes through you, most flesh allows it to pass through with minimal refraction, but it doesn't go through your bones as easily.
Radio waves have less penetration power than x-rays. The planet is considerably denser than you, and it gets denser the deeper you go.
In fact, not even higher-energy radiation like gamma rays would get through the earth. You'd need neutrinos for that, but then, that's not electromagnetic radiation and no, there is no technology to use those to communicate (yet).
Long-range radio communication will usually work with waves that reflect on the ionosphere, have the waves being sent in a very tight beam (you get more range for the same power this way, when compared with omnidirectional transmission), or use relays. It is very usual, for example, to combine the latter two strategies by using sattelites.
