Collision system that checks if there is a collision every frame are the most common so I want to know if there is any famous game that uses the opposite.

To clarify, what do you mean by not checking every frame? Do you mean systems that predict when the next collision will be and don't check again until then?

yes

You can do it in simple games, but I doubt it is possible in the most complicated cases. User interaction and complicated forces makes it really hard to predict something.

there are physics engines which use continuous collision detection, i.e. the times of contact are calculated. But they still run with a fixed time step. After all the physical quantities can change every frame due to user input.