Also, don't the newer Priuses (Prius', Pri-i, Priusi?) or some other hybrid have that 'feature' where they turn off at stoplights?
The Prius, like most (all?) hybrids, only uses the gas engine at higher speeds. At lower speeds, it's an electric motor. So when the car is not moving, the motor isn't running. It's not a feature so much as how an electric motor works.
I'm going to take the opportunity to nerd out about Hybrid systems a bit as a clarification.
Some (like the Nissan Crossover systems, Murano, Pathfinder, etc) will still use the gas motor 100%. The electric motor is effectively a large starter that can also support acceleration and regenerative braking.
The modern Prius is one of the more advanced systems and will allow full EV upwards of 30mph (many don't past 5 or 10mph) under the right circumstances. And will sometimes (again correct circumstances) shut down the gas engine when it isn't needed (long stop lights, long downhills, etc). There is an insane amount of programming that goes into these hybrids. It depends on outside temp, climate control settings, battery temp, battery charge status, and even driver habits.
Some gas-only engines (Ford Fusion, Dodge Ram V6) also have a a gas engine shut off feature for stop lights, Often called an idle stop start/ISS. These systems will shut the engine off under very specific circumstances to save gas in city driving. A key criteria for engine shut off in all hybrid/ISS systems is AC on/off, as most of these vehicles have belt driven compressors that need the engine to be running to provide cooling. Again the Prius being a more advanced hybrid actually has an electric AC compressor that can keep cooling even if gas engine is off.
Obligatory MMM comment: bikes are better