Here is the purpose of the 3rd prong/ground wire:
An appliance or tool that has a metal enclosure, or any metal part that someone can touch that could accidentally become energized, will generally have a 3 prong cord. If a live wire inside the appliance were to come loose and touch the metal enclosure, the circuit breaker protecting the outlet will trip. Without the 3rd prong, the circuit breaker will not trip and the enclosure of the appliance will just stay energized, and you'll get a shock when you touch it.
Here is the reason the breaker trips if the live wire touches the grounded enclosure:
If you connected the hot leg directly to the neutral wire (NOT the ground, the neutral), you'd have a dead short. A dead short = a LOT of current going through the wires. When there's a lot of current going through the wires, the breaker trips. (A 15 amp breaker will trip anytime the current goes over 15 amps, that's why it's a "15 amp breaker!")
The ground wire is bonded to the neutral bar in the breaker panel. So, if the hot leg contacts the ground wire (or a grounded enclosure), it's essentially the same thing as the hot leg contacting the neutral wire and also results in a dead short. This makes the breaker trip as soon as possible, thus de-energizing the appliance and eliminating the shock hazard. This is NOT to say that the ground wire is the same as the neutral wire, and you CANNOT simply use the neutral as a ground wire. The ground wire is to remain "dead" at all times and ONLY used to clear faults!
And this hopefully clears up the misconception that the ground wire sends current to "the ground" (the literal ground you stand on). The ground rods you have going into the ground serve a completely different purpose. The ground wire doesn't send fault current to the ground rods, it sends it back to the source (the transformer), the same place that the hot legs and neutral originate. Remember, the goal is to essentially create a short circuit between the hot leg and the neutral, which both come from the transformer, NOT "the ground."
I really hate those 2 prong adapters. They serve no useful purpose, if you use them the way they were designed (which NO ONE ever does), and they're just plain unsafe if you use them improperly (which EVERYONE does). You're supposed to connect the round tab on the adapter to the screw that holds the outlet cover plate on (which no one ever does). Not connecting this tab is unsafe because if the exposed parts of the appliance become energized, the breaker won't trip and you'll get shocked if you touch them. Even if you DO connect the tab to the cover screw, it still won't do anything if the outlet box is not bonded to ground!
If the outlet box IS bonded to ground, then there's no reason you can't just swap out the 2-prong outlet for a 3-prong outlet and just bond it to the outlet box, thus eliminating the need for those stupid adapters. And that is why I hate those adapters.