It’s been a thing. My car is 20 years old and requires it. Engines with higher compression require higher octane fuel to reduce pre-detonation and pinging. Using low-octane fuel in one of them can cause game-ending physical damage to the engine.
Many more modern cars can sense lower-octane fuel and adjust for it, at the cost of power and efficiency (i.e., mileage).
Some vehicles, especially ones with OEM performance tuning, run high compression ratios or forced induction. Higher octane gas allows for more compression within the piston before ignition. I had a 2003 Toyota Matrix that redlined at 9100 rpm and used their fancy Toyota variant of VTEC that would dynamically swap the camshafts on the engines past a certain RPM. Although the engine was naturally aspirated (no turbo), it had the compression ratio of 11.5:1, which is pretty high for an economy vehicle (1.8L)
The octane rating you see on gas indicates the pressure at which gasoline will combust. Engines tuned to a higher compression to ignite require higher octane level gasoline. Using something other than what the engine is tuned to might put a lot of extra wear or degrade performance of the engine.
The gasoline will ignite before it is supposed to, forcing the piston back down before it has travelled all the way to the top of it's stroke. The engine will destroy itself. You can hear "knocking" coming from the engine when this is happening. It's worse than it sounds.
I know this is definitely true of older engines that aren't controlled by fancy software, but I suspect at least many consumer cars are capable of adjusting to the difference. I could be wildly wrong here though, and wouldn't want to test it myself.
All the comments are giving unequivocal yes’s, I’ll note that some cars (my buddy’s Subaru) will say they require premium but work just fine without. Currently going 240k miles still strong.
A car with knock sensor will detect lower-quality fuel and pull back timing. This will usually limit your power, but not damage your car. My car manual even explicitly states that it won't affect engine lifetime.
Full disclosure, I still use premium anyway because I want to keep the car for a long time and I don't fully believe this disclaimer.
Generally you'll get worse fuel economy due to the ECU and knock sensor detecting the lower grade fuel and pulling ignition timing out. It's unlikely you'd even save money at the pump
Many more modern cars can sense lower-octane fuel and adjust for it, at the cost of power and efficiency (i.e., mileage).