TVs are especially bad, in the default mode some of them have ~200ms input lag. "Game Mode" usually brings it down to more like 20ms though.
Edit: did a google, don't know how accurate these are: https://www.rtings.com/tv/tests/inputs/input-lag
It seems most get under 20ms lag when put into game mode, which I'd think is what matters to most people. At that point, when it isn't daisy-chained with any other lag (so a wireless controller delay will make a difference), it's imperceptible to me. I am not a professional gamer though, and from what I understand the higher refresh rates that pro gamers use (such as a 240 Hz monitor) have measurable improvements in their performance as gamers.
A 20ms response time still means the signal is dropping every fifth frame in a 60 fps game.
An excellent gaming screen like a PG258Q might have GTG of 1 ms but at the full 240 Hz it still has about 5 ms of input lag.
Such a setup isn't cheap, but it's far more reliable and space-efficient than a giant CRT.
That said, I still generally prefer to use my PVM CRT monitor for gaming for reasons already discussed in this thread. It really can't be beaten.
