This depends a lot on the circumstances that are present.
Many definitions of electricity will state that it is the flow of electrons through a conductor. If this is what you mean then under everyday circumstances electricity will not pass through glass. This is equivalent to saying that direct current (DC) electricity does not pass through glass or any other insulating material. Under very extraordinary circumstances where the voltage difference between one side of the glass and the other is extremely high, electrons can flow across the glass. This probably wouldn't last very long as the heat generated would probably melt the glass or cause it to break. If you imagine a bolt of lighting going through the glass you will have a good idea of what I'm talking about. The thinner the glass is, the lower the voltage difference will need to be, and vice-versa, the thicker the glass the higher the voltage difference must be.
If you don't require electrons to flow across the glass then there are other circumstances where you can see electricity pass through glass. As you may or may not know, electricity is associated with electric and magnetic fields. Electrons are charged particles which means they are surrounded by an electric field wherever they go and they can be pushed around by electric fields produced by other charged particles. When electricity is said to flow in a wire it means there are electrons moving in the wire and the electric field of the electrons will be surrounding the wire. While electrons can't go through glass, electric fields can. If you collect a bunch of electrons on one side of a piece of glass, their electric field will penetrate the glass and be felt by electrons on the other side of the glass, if it is not too thick. You can create this situation easily by placing a thin sheet of metal flat against each side of the glass. You then connect a battery to each of these metal plates using metal wires. Electrons will collect in the metal plate on the side of the glass connected to the negative terminal while electrons will leave the plate connected to the positive terminal. Electricity will flow through the wires until the battery can no longer force any more electrons onto the negative plate and can no longer pull any more electrons off the positive plate. At this point no more electricity will flow but if you were to reverse the battery terminals, the electricity would flow again but this time in the opposite direction until the same stopping point was reached. If you could arrange it so that these battery terminals were reversed on a regular basis, it would seem as though the electricity was constantly flowing. This is exactly what happens whey you are using an alternating current (AC) generator instead of a battery. There is nothing special about the glass in this example, any insulating material would work. You could use rubber, plastic, air, etc. This setup is actually very common and found everywhere in electrical devices where it is called a capacitor and the insulating material is called the electrolyte of the capacitor.
You might think that using an AC generator is a cheat as the generator is connected to both sides of the glass. Its like pumping water back and forth from one side to the other of a glass barrier. The water never goes through the glass. You may be more impressed, however, if we were only pumping water on one side of the glass. If the water level increased and decreased on the pump side of the glass and all by itself the water on the other side were following suit. While this doesn't work for water, it does work for electricity. If you only hook up the negative terminal of a battery to one of the plates attached to the glass, that plate will collect electrons and at the same time electrons will leave the plate on the other side of the glass which has nothing connected to it.. This will stop just like before when the battery can't push any more electrons onto the plate. You could then connect the positive terminal instead and the flow would reverse, ON BOTH SIDES OF THE GLASS! Connecting an AC generator to just one side would also cause electrons to move onto and off of the unconnected plate continuously. The reason for all of this is that the electric field from the electrons pushed onto the plate on one side of the glass will push the electrons on the other side away from the glass and off the plate. When you pull the electrons off the plate on one side, the plate will have an effective positive charge which will attract the electrons onto the plate on the other side of the glass.
There is one other way that electricity can be seen to pass through glass. In this case it is due to the magnetic field that electricity produces. A magnetic field is produces whenever charged particles are moving and, in addition, charged particles can be made to move whenever a changing magnetic field is present. What you can do is attach metal wire to both sides of a piece of glass so that it lays on the surface of the glass. You want to cover as large a region of the glass surface as you can with the wire as close to itself as you can get it without touching. You also want the patches of wire on each side to be directly across from each other. If you connect an AC generator to one of these wire patches the electrons (charged particles) will move back and forth in the wire of the patch and this will produce a changing magnetic field that will penetrate the glass and surround the wire of the patch on the other side. The changing magnetic field will make the electrons in the wire patch on the other side move back and forth just like those in the wire connected to the AC generator. This is another case where DC electricity doesn't work because while DC electricity does produce a magnetic field since the electrons (charged particles) are moving, that magnetic field can't make other electrons move because it isn't a changing magnetic field.
Many definitions of electricity will state that it is the flow of electrons through a conductor. If this is what you mean then under everyday circumstances electricity will not pass through glass. This is equivalent to saying that direct current (DC) electricity does not pass through glass or any other insulating material. Under very extraordinary circumstances where the voltage difference between one side of the glass and the other is extremely high, electrons can flow across the glass. This probably wouldn't last very long as the heat generated would probably melt the glass or cause it to break. If you imagine a bolt of lighting going through the glass you will have a good idea of what I'm talking about. The thinner the glass is, the lower the voltage difference will need to be, and vice-versa, the thicker the glass the higher the voltage difference must be.
If you don't require electrons to flow across the glass then there are other circumstances where you can see electricity pass through glass. As you may or may not know, electricity is associated with electric and magnetic fields. Electrons are charged particles which means they are surrounded by an electric field wherever they go and they can be pushed around by electric fields produced by other charged particles. When electricity is said to flow in a wire it means there are electrons moving in the wire and the electric field of the electrons will be surrounding the wire. While electrons can't go through glass, electric fields can. If you collect a bunch of electrons on one side of a piece of glass, their electric field will penetrate the glass and be felt by electrons on the other side of the glass, if it is not too thick. You can create this situation easily by placing a thin sheet of metal flat against each side of the glass. You then connect a battery to each of these metal plates using metal wires. Electrons will collect in the metal plate on the side of the glass connected to the negative terminal while electrons will leave the plate connected to the positive terminal. Electricity will flow through the wires until the battery can no longer force any more electrons onto the negative plate and can no longer pull any more electrons off the positive plate. At this point no more electricity will flow but if you were to reverse the battery terminals, the electricity would flow again but this time in the opposite direction until the same stopping point was reached. If you could arrange it so that these battery terminals were reversed on a regular basis, it would seem as though the electricity was constantly flowing. This is exactly what happens whey you are using an alternating current (AC) generator instead of a battery. There is nothing special about the glass in this example, any insulating material would work. You could use rubber, plastic, air, etc. This setup is actually very common and found everywhere in electrical devices where it is called a capacitor and the insulating material is called the electrolyte of the capacitor.
You might think that using an AC generator is a cheat as the generator is connected to both sides of the glass. Its like pumping water back and forth from one side to the other of a glass barrier. The water never goes through the glass. You may be more impressed, however, if we were only pumping water on one side of the glass. If the water level increased and decreased on the pump side of the glass and all by itself the water on the other side were following suit. While this doesn't work for water, it does work for electricity. If you only hook up the negative terminal of a battery to one of the plates attached to the glass, that plate will collect electrons and at the same time electrons will leave the plate on the other side of the glass which has nothing connected to it.. This will stop just like before when the battery can't push any more electrons onto the plate. You could then connect the positive terminal instead and the flow would reverse, ON BOTH SIDES OF THE GLASS! Connecting an AC generator to just one side would also cause electrons to move onto and off of the unconnected plate continuously. The reason for all of this is that the electric field from the electrons pushed onto the plate on one side of the glass will push the electrons on the other side away from the glass and off the plate. When you pull the electrons off the plate on one side, the plate will have an effective positive charge which will attract the electrons onto the plate on the other side of the glass.
There is one other way that electricity can be seen to pass through glass. In this case it is due to the magnetic field that electricity produces. A magnetic field is produces whenever charged particles are moving and, in addition, charged particles can be made to move whenever a changing magnetic field is present. What you can do is attach metal wire to both sides of a piece of glass so that it lays on the surface of the glass. You want to cover as large a region of the glass surface as you can with the wire as close to itself as you can get it without touching. You also want the patches of wire on each side to be directly across from each other. If you connect an AC generator to one of these wire patches the electrons (charged particles) will move back and forth in the wire of the patch and this will produce a changing magnetic field that will penetrate the glass and surround the wire of the patch on the other side. The changing magnetic field will make the electrons in the wire patch on the other side move back and forth just like those in the wire connected to the AC generator. This is another case where DC electricity doesn't work because while DC electricity does produce a magnetic field since the electrons (charged particles) are moving, that magnetic field can't make other electrons move because it isn't a changing magnetic field.