The answers to this this question make it clear how modern airliners dump fuel in the case of an emergency. As far as I understand, fuel dumping might be done to lower an aircraft's weight to the maximum landing weight, particularly soon after takeoff. As far as I understand, jet fuel is typically not safe. When I, as a complete outsider, hear of fuel dumping, I imagine a whole bunch of dangerous corrosive fuel being dropped on whatever happens to be below, and it sounds like a frankly awful idea. What makes fuel dumping safe, or if it is dangerous what makes it worth it?
Fuel dumping is almost always an emergency maneuver, and it is never good for the environment. So the alleged danger from the dumping must be balanced with the imminent danger to the 200–400 passengers involved. It is never an easy decision but that's why the Captain gets paid the big bucks...
Dumping fuel sounds dangerous but it is not. It is not going to explode. Jet-A can be compared to kerosene and I don't have that statistic so let's compare it to Diesel Fuel which is not dissimilar to Jet-A. Diesel Fuel at 400°F(204°C) is as volatile as gasoline is at 70°F(21°C). Obviously that is a big difference. Jet-A also evaporates into the air, so little if any hits the ground.
The biggest danger I see is to the atmosphere.
It's not really safe in an environmental sense, but it's not that bad. Jet fuel is essentially kerosene, which is harmful, but as far as engine/industrial fluids go, it's pretty benign. Additionally, when an airplane dumps it, it's diluted so much by the time it makes it anywhere that it's not a significant concern anymore.
On the flip side, if an airplane didn't dump fuel and landed overweight, the potential side effects could be disastrous and could result in many injuries and damages.
Basically, it's choosing between two bad options, landing overweight or dumping fuel, and dumping fuel is the least bad of the two of them.
In any case, it's quite a rare occurrence. You are exposed to far more toxins just walking down the street of a city than from airplanes dumping fuel.
Up-voting @skipmiller, I offer this addendum
Emergency Landing After Takeoff
Large aircraft typcially cannot land as heavily as they can take off. It's a structural issue. So fuel dumping would be done if an emergency did not allow the time to burn down to allowable landing weight.
Maintain flight with engine/power loss
If available power did not allow sustained flight one might dump fuel. Worse if you were over mountains and needed to stay high.
There was a case of a C-130 - a high wing plane - ditching in the Atlantic. It floated for a couple days with empty gas tanks and had to be shelled to force it to sink.
If a wing tank fuel leak was causing aircraft balance problems one might dump from the opposite wing to keep the aircraft controllable.
Life Imitating Fiction
15 minutes after takeoff we lost all thrust on 3 engines. Our gross weight forced us into a controlled descent. Dumping most of our fuel might very well have kept us airborne on 1 engine, if not I think empty tanks would have limited possible fuel fire in the controlled crash. I was about to dump 45,000 lbs of JP-4 all over west Texas when we solved our engine problem.
Fuel dumping is done by many types of Aircraft(fighter etc.) it is not limited to the role(cargo, passenger etc.). Although the purpose may be same.(Sometimes its done to reduce the load, to avoid any accident).
In a fighter plane fuel is dumped to reduce the weight and increase the distance to cover(the weapons it carries already has tons of weight on the plane). This could be the same in passenger but situations may vary.
Fuel dumping is really a serious threat to the environment or the biological impact especially if it's dumped in the water(causes damage to maritime species and irreversible damage to the coral reefs if present).