Does the Toyota Prius stop if driven off without the key inside?

This video tells you a lot.

Basically, this cannot happen. The Prius knows where the key is at. If the key is on the outside of the vehicle, it won't start, period. If the key is too far away, it won't even unlock. If the key is left inside the vehicle and you try to lock the door, it won't let you.

Toyota engineers have thought a lot more about this than other car manufacturers have. There was an episode of Top Gear where the three guys came to the states and drove modern American muscle (Corvette, Mustang, & Challenger). Jeremy Clarkson was driving the Challenger. He parked it outside of a restaurant then went inside and sat down very near where the car was parked. One of the other two guys went outside, got in the Challenger, started it, then drove it out into the middle of the street before it died (from being too far away from the remote). Quite some hilarity. Point is, you couldn't even get that far in your Prius.

I don't believe you have anything to worry about.

Your concern is valid. This article gives a good description of the weakness of smart keys. A man in the middle attack can fool the car to think that the key is inside allowing it to start. Once the car is running it won't shut off if the key leaves the car. These keys are battery powered and if that battery dies while you are driving on the highway it may be dangerous if the car just shuts off.

Don't forget that this method takes two people and one of the people has to stand next to you for some time. It's just as easy to steal you keys or purse.

Not a specific answer for a Toyota Prius, but:

This summer, we had an incident here in Germany, where the motor stopped after throwing the key out of the window.

There's an online police report, so this is not a hoax.

Here is my short translation:

A 33 year old mother was driving her VW Passat on the highway (German "Autobahn") A1 near Lübeck with her 1.5 year old daughter on the right rear seat. As the daughter was whining due to tiredness, the mother gave her the key ring with the ignition key to play with. As the daughter didn't calm down, the mother opened the window a little, hoping the fresh air would help.
The daughter threw the key out of the open window, causing the motor to stop. The car was still steerable and the mother managed to stop on the emergency lane. The mother called the police, who searched for the key ring and finally found it. All keys including the ignition key were damaged, but the electronics survived, so the mother was able to drive home.

So, this was a Volkswagen, not a Toyota, but it shows that bad thinks can happen.

Of course, the behavior of the car depends on what the engineers implemented and may vary from brand to brand, or from car to car.
In my personal mind, the motor should not stop while driving, but on the next halt.

Paulster2 wrote: "Basically, this cannot happen. The Prius knows where the key is at. If the key is on the outside of the vehicle, it won't start, period."

This is not true, however.

Here we speak about thief(s) trying to steal your car. They will use the wireless amplifier to create the link between the car and your key (which is in your possession, at home). The car will unlock, thief No. 1 steps in, the car will recognize "key inside" situation and your car will start.

There is a nice video on YouTube.

Stealing the modern car packed with electronics is quite simple and fast. Prius is not an exception. These systems can be fooled too easily and cannot be trusted. Period.

It just happened with our company-owned 2011 Prius. We had two drivers (one a trainee) in the vehicle, when a long-distance job came in. The second driver got dropped off at the office, while the first driver did the delivery, except that the key fob was in the second driver's coat pocket. There was no problem until the 1st driver, now 40 miles away tried to restart the engine after making her delivery. So the Prius can go at least 40 miles without a key fob, as long as the engine is already running when the key leaves the vehicle.