With higher refresh rates, you are able to see more frames, feel more responsive when mousing, and relieve your eyes from flicker. Flicker-free is considered 85Hz. However, this only applies to CRTs. LCDs get a little more complicated. Now it depends on your pixel response time. All the benefits of the above are applied except that higher refresh rates won't affect your the comfortness of your eyes as with CRTs. I would keep the refresh rate below the pixel response time, if possible, but never diverge from your monitor's optimal settings.
With CRTs, you will have to decide which is more important, higher refresh rates, or higher resolutions. However, I strongly recommend that you don't set your refresh rate lower than 85Hz.