Here's a free product idea that I offer freely to the world. This would be a wonderful safety and energy conservation feature for a stove that I would seek out when making my next purchase.
Imagine a stove with a light sensor. It knows when the kitchen lights are on and when they're off. It would be able to calibrate itself to know what's "on" and what's "off" by simply observing normal light levels. There may need to be two in different places on the stove, since in certain kitchens it might be common for one side of the stove to be obscured by shadow, but not the other.
Now, whenever you turn off the lights, this kitchen will wait a couple seconds, and if either of the burners or the oven are on, it will emit a series of beeps and then blink a "snooze" button. If you really wanted the lights off but the stove on, you could press snooze to make it not beep again for eight hours.
Tada. No one would ever forget and leave their burners on again.