What are the risks of jump-starting a modern car?

Blown fuses from backwards polarity cable installation is the most cause of vehicle damage at this time.

The risk of explosion is lower than in older battery designs due to less venting of hydrogen gas in current designs. It can still happen and should be guarded against. The most common injury is blindness due to acid burns.

The concern in the question from jump stating is that of high amperage arcing causing power to flow through the ground side getting into the circuits in the many IC circuit controlled devices on modern vehicles. Even in this case the risk is low; partly due to better ground side surge protection in the devices and low incidence of arcing during connection. One can reduce the risk of damage by one of two ways.

1) Remove both cables from the battery before connecting to the alternate power source, this is the guaranteed way to ensure no problems.
2) Use a modern battery charger with a "soft start" feature that slowly applies power when turned on.

That said, we still use jump boxes daily with no problems. Ensuring that the key is off and the cable polarity is correct. We do not use other vehicles as the power source and do use a soft start charger whenever possible.

There is absolutely no reason for a car to break down because of jump starting if:

1- The cables were connected correctly. Cars use same voltage etc.

2- The battery is not broken (eg. cant accept charge anymore)

1 is obvious. The reason for 2, if battery cant absorb energy, removing jump leads can lead to a voltage spike and this is of course harmful. You would have same effect if you disconnect the battery of a car while engine is running.

So, it is safest to charge the empty battery and then restart the car on its own power. Because you can also see if your battery can hold charge (absorbing power) or not.

Here, you have to understand that the problem is not related to soft start charging, arcs etc. It is not even related to jump starting. Considering if you did everything else right. The only dangerous part left is removing the jump leads. Do a web search for "removing battery when car is running". If your battery is completely broken, you may have the same effect when removing jump leads. Because you are disconnecting the donor battery which may be the only working battery in system.

I found this thread to be interesting also : Jump Start Destroying the Electronics - Myth?

I believe most often the damage is caused by people too tired or dumb enough to connect cables wrong way but not even realizing it even afterwards, then thinking that jump starting broke their car and then telling this story to others. I bet many do not even know that it is important to connect + to + and - to - . It takes only one person to tell that jump starting broke his car and the fear spreads like a disease.

I also think that in the past some people attempted jump starting 12V systems with 24V systems then decided jump starting is dangerous for electronics...

In addition, of course marketing departments are not helping either. They know that people are scared of jump starting cars because of electronics damage, wrong connections etc. So, they promote the fear even more so they can make sales on expensive cable sets. Honestly, probably the cables which can detect incorrectly made connections and refuse to work are probably useful in case you are color blind or in case if the user is expects that the cable will do everything for them automatically.

When all these information is passed from person to person, some of the facts are lost and usually one thing is left : 'jump starting broke the car'. Of course when the factors leading to result are lost, and you do not have understanding of how electric behaves, it is easy to believe in this myth.

Also some fun info, do not use defibryllator to jump start your car : MythBusters - Defibrillator Jumpstart

Damage can come to the person's car who's providing the boost. I have seen blown alternators and other damage. The only lower risk way is disconnect the supply battery from the car. It will clear electronics settings doing this. These days I suggest getting a Lithium battery booster. I'm in my 50's unfortunately I have to turn people down if they want a boost because of damage.

I laugh when I read these commits after being in the Auto Electric business for years as nobody knows why systems get blown while jump stating them. If you every worked on systems with relays on them to handle the high current flow know what happens when you turn that relay off. If you turn that relay off against an operating alternator you can blow it. When the plunger returns back through the windings used to close it AC current is generated and is in the exciting wire of the relay which can jump to jumper cables and etc. In the main system it is in the alternator does not fire up until later. So if the car you are jumping doesn't have a filter to kill this voltage it can cause a lot of damage.