The Ground wire is purely for safety, and carries no current during normal use.
The Neutral wire is responsible for carrying all the "return" current the Hot wire provides to the electrical device.
The neutral wire is not, however, a perfect conductor, and has some resistance. A 100 foot run of 14 awg wire, for instance, has 0.25Ω resistance. If an electrical device is using the full 15 amps maximum load allowed on that wire, then at that load the neutral line will be a little more than 3 volts away from ground.
3 volts AC isn't a lot, but it can be noticeable if you happen to touch it, and under some circumstances it can be fatal. Further, without ground, it's one failure point away from having a full 120V available on it. For instance, if it's at the end of the circuit and has a number of daisy chained outlets in the path, the resistance goes up significantly, increasing the voltage level under load, and increasing the chances of a poor arcing connection at one of those locations.
It's the reason why ungrounded equipment (two prong plugs) is designed to be fully insulated from the user - even though neutral is near ground, it isn't ground and depending on the connection quality along the way to the panel and the load on the line, it may be dangerously far from ground.
If you place a highly reactive load at the end of the line (motor, switching power supply, etc) that uses the full current capacity of the line (you'll notice that these types of loads are almost always grounded) then you'll find that the neutral line is carrying a waveform that may be far from safe, even though, technically, it's a very low RMS AC voltage.
Never, ever treat the neutral line as safe.