One of my screens is a 144 Hz monitor. On games that I can go above 60 fps it makes a noticeable difference in the smoothness of action. Even just dragging around a window really fast is a noticeable difference between a 60 Hz monitor.
Any game made for PC capped at any frame rate is a lazily ported piece of stuff.
That said I can deal with at least 30 fps if my PC can't render any faster. I play GTA V at around 50 fps for example.