Why is glass transparent? Once I asked this question from my teacher and he replied "Because it passes light.". "And why does it pass light?" I asked and he said, "Because it is transparent.".
The same question again, Why glass is transparent? Why does light pass through it, while for opaque objects, it does not?
 A: Photons pass through glass because they are not absorbed. And they are not absorbed because there is nothing which "absorbs" light in visual frequencies in glass. You may have heard that ultraviolet photons are absorbed by glass, so glass is not transparent for them. Exactly the same happens with X-rays for which our body is nearly transparent whilst a metal plate absorbs it. This is experimental evidence.
Any photon has certain frequency - which for visible light is related to the colour of light, whilst for lower or upper frequencies in the electromagnetic spectrum it is simply a measure of the energy transported by photon. A material's absorption spectrum (which frequencies are absorbed and how much so) depends on the structure of the material at atomic scale. Absorption may be from atoms which absorb photons (remember - electrons go to upper energetic states by absorbing photons), from molecules, or from lattices.
There are important differences in these absorption possibilities:


*

*Atoms absorb well-defined discrete frequencies. Usually single atoms absorb only a few frequencies - it depends on the energetic spectrum of its electrons. Regarding atomic absorption, the graph of absorption (plotted as a function of frequency of light) contains well-defined peaks for frequencies when absorption occurs, and no absorption at all between them.

*Molecules absorb discrete frequencies but there are many more absorption lines because even a simple molecule has many more energetic levels than any atom. So molecules absorb much more light.

*Crystalline lattices may absorb not only discrete frequencies but also continuous bands of frequencies, mainly because of discrepancies in the crystalline structure.


As glass is a non-crystalline, overcooled fluid, consisting of molecules, its absorption occurs in the 1st and 2nd ways, but because of the matter it is composed of, it absorbs outside our visible spectrum.
A: Essentially because of absorption. When photon flies into the material it interacts with its constituents. This interaction can be divided into two contributions. One of them is elastic and is the source of the index of refraction (because effectively it just slows the photon down) while the other one is inelastic. Photon gets absorbed by an atom (say) and later it is emitted as thermal radiation in random direction thereby losing the original information it carried.
When you look at this macroscopically, this process will be described by some parameter like penetration depth and intensity w.r.t. depth will decay exponentially. So if you made opaque objects thin enough, they would still be transparent (although the outgoing light would be weaker depending on thickness). Of course, this discussion completely avoids surface effects (reflection, refraction, scattering, etc.).
Note that all of this depends on frequency of the incident light. Atoms (let's just talk about them for simplicity; in reality there will be contribution also from molecules, lattice, free electrons and whatnot) have something called absorption spectrum. This arises because for certain frequencies electron can catch the photon and get excited to the higher energy state. So, while a material can be transparent in certain range of frequencies (like glass is for visible light) it can be quite opaque in others.
A: This may be a little technical, but I always thought it was cool: one of my professors once pointed out that transparency only happens because the material is (approximately) a linear dialectic over the frequency range that you care about.  Turns out water is a linear dielectric over precisely the range of frequencies our eyes can detect.  coincidence?
A: There is a lot of nonsense around about this. It is NOT a very thick stiff or cold liquid, nor is it due to how ordered the structure is. In simple terms it is all about the electrons in the substance. When photon of light enters a substance, it will interact with an electron changing its energy state. 
KEY POINT — Electrons can only exist in fixed (banded) energy levels.
In common opaque material, it takes a small amount of energy to move the electron from its resting energy state to a higher energy state, so the low energy photon of visible light is absorbed, transferring its energy to the electron which in turn moves to a slightly higher energy state. 
In much rarer transparent material the distance between the electrons rest energy level and the next higher state is much much greater. So because the electron can only be "resting" or at a high energy level NEVER in between, the little photon of visible light doesn't carry enough energy to transfer to the electron to make it jump to the higher state. So it keeps its power, doesn't get absorbed and passes through the material. Hey presto, see through.
Some glass only lets through light of a certain colour. This is because different colour light haas different energy levels and so depending on the energy needed to 'move' electrons to a higher energy state some colours will be strong enough and absorbed and others wont and will pass through 
NOTE, I am simplifying a bit, for example it doesn't literally 'pass through' as such, the the way the electron and photon interact are quantum mechanical and none of this includes  polarization, reflection etc. all of which works on a quantum level. That said on a macro scale, without the quantum detail (which would take years to teach) this is what is happening.
A: There is no absorption and re-emission process when light travels in a transparent medium. Medium does absorb some portion of the light, but no re-emission happens, or re-emission is so small that it can be neglected. 
The absorption doesn't make electrons to transit to higher energy levels, but to increase their kinetic random movement, including atom's random vibration. This results in increased temperature of the glass.
Some fluorescent substances absorb visible light and re-emit it. When this happens, after the visible light is turned off, the matter has its own light emitted for a while. This involves electron energy levels transition.
A: This answer is a little circular and like Burley's. Transparent materials have uniform electromagnetic coupling between its molecules. Think of glass as a uniform array of tiny capacitors. 
