I want to jump in here and add particularly to Augie and kwired.
Do a little research on transformers, particularly single phase center tapped, and 3 phase 4 wire Wye connected transformers. While doing this remember that for all intents and purposes, electricity "flows" similar to a liquid in a closed system. The winding of the transformer is part of that closed system. For this, don't worry at all about the primary side, for the time being. Single phase is easier to understand first. Follow one electron.
If your load (equipment) is 240 volts, the electron starts at whatever point inside the transformer coil you want. It leaves along a wire, runs along the wire, runs through the motor, causing it to operate and then runs along the other wire back to the coil, then through the coil to the original start spot.
If your load is 120V similar to the above, except one of the wires is the neutral. I don't like to say go and return, because the direction changes 60 times a second. As you can see, the path to ground is a dead end, in either of the above scenarios, so the electron WILL NOT flow to ground.
Now is gets complicated. If you have both "hots" going out, with a shared neutral coming back, any time only one load is on, the 2nd scenario above works, but when you turn on the second load, now, as electron flow, basically they will travel, along a wire, through one load, along the neutral, until the come to the common joint, where the neutrals for each load join together. At that point, think of it like as many electrons as the second load will allow to pass (in other words, the amount of amperage) will flow, back up the neutral wire to the second load, and then along the hot wire, back to the transformer coil. Only the extra electrons, that the second load can't use will flow back to the transformer on the neutral. Note that the 1st load is the one the draws more current (amperage). Now you know why one of the terms for the neutral is the common.
Bonding the neutral to ground. What that does is for safety 100% period. As I pointed out, in all of the above scenarios, any electron trying to run to ground can only do it on the bonding wire, and that is a dead end. When and if, a fault allows the electrons to run to a metal case of equipment, or a water pipe, instead of just sitting there, waiting, to zap the unsuspecting victim, it will instead run back to the transformer coil along the grounding system. Basically, the path is designed to be big enough that the current will cause the breaker to trip, negating the danger. The other part of this is that the possibility of a human contact the full voltage of the system (Hot to hot, or direct short) is far more unlikely without two faults. In an ungrounded system, it basically takes two ground faults to trip a breaker, but all the time that the single fault is out there, the potential for a person to become the second fault is really high, because you can't "see" the first fault. Military ships, operate on ungrounded systems, because reliability is more important than human life. They have sensors that sense the first fault, but the systems will still operate until the crew ahs time to fix the fault, which may not be in the middle of a conflict.
All of these answers are IMHO.. 