Some games have their own refresh rate settings. Note if you have an LCD montor refresh rate is kind of null.
But as a general rule, 75hz is a decent and common refresh rate. Any lower like 60hz and below, may bother your eyes after a while.
Note also that changing refresh from 70hz to 80hz or whatever, is NOT really something you "notice" anyway.
Refresh rate isn't related in any way to FPS in a game if that's what you're thinking. Game play won't change based on monitor settings. In that one refresh rate will yeild more FPS.
Resolution may affect games, as a larger resolution, color depth, and perhaps a very fast refresh rate, makes your video card have to work harder.