What kind of cooktop heats almost instantly and then doesn't burn immediately after you remove the pot?

I think it’s called induction. A glass top, right?
Very expensive.
We should all invest in these though they take getting used to because it’s a different kind of cooking. The pan heats up instead of the stove surface. This is many times more efficient than, say, the dangerous, pleasurable open flame you get with a gas stove.

From http://theinductionsite.com/how-induction-works.shtml

Put simply, an induction-cooker element (what on a gas stove would be called a “burner”) is a powerful, high-frequency electromagnet, with the electromagnetism generated by sophisticated electronics in the “element” under the unit’s ceramic surface. When a good-sized piece of magnetic material—such as, for example, a cast-iron skillet—is placed in the magnetic field that the element is generating, the field transfers (“induces”) energy into that metal. That transferred energy causes the metal—the cooking vessel—to become hot. By controlling the strength of the electromagnetic field, we can control the amount of heat being generated in the cooking vessel—and we can change that amount instantaneously.

We have two portable ones for our prep kitchen downstairs. To the best of my recollection, they cost about $100 each. Ceramic top, not glass. They are cool!

My dad used to have one of these in his kitchen. It was a bit different to cook with as susanc said, but i liked it a lot more than gas. Everything cooked a lot faster and there was less waiting on stuff. Sadly he no longer has it since he was in the kitchen one day (not even cooking) and the whole stove just shattered out of no where. He looked into getting a new one, but the cost was just too high so he went with gas.