Does it make sense having FPS higher than the monitor refresh rate?

I've heard that the human eye processes twenty-four images per second. Also, monitors usually work with 60Hz.

My question is, for a highly interactive application (e.g., a fast-paced FPS game) does it make sense to render faster than the monitor refresh rate?

Wikipedia: "A certain amount of discarded “headroom” frames are beneficial for the elimination of uneven (“choppy” or “jumpy”) output, and to prevent FPS from plummeting during the intense sequences when players need smooth feedback most.

Aside from frame rate, a separate but related factor unique to interactive applications such as gaming is latency. Excessive preprocessing can result in a noticeable delay between player commands and computer feedback, even when a full frame rate is maintained, often referred to as input lag.

Without realistic motion blurring, video games and computer animations do not look as fluid as film, even with a higher frame rate. When a fast moving object is present on two consecutive frames, a gap between the images on the two frames contributes to a noticeable separation of the object and its afterimage in the eye. Motion blurring mitigates this effect, since it tends to reduce the image gap when the two frames are strung together The effect of motion blurring is essentially superimposing multiple images of the fast-moving object on a single frame. Motion blurring makes the motion more fluid to the human eye, even as the image of the object becomes blurry on each individual frame.

A high frame rate still does not guarantee fluid movements, especially on hardware with more than one GPU. This effect is known as micro stuttering."

Hope that helps a little.

If the FPS rate of the game is higher than the monitor's refresh rate, some of the rendered frames are never shown and the time and processing power used rendering them is wasted.

Most rendering engines never go higher than the refresh rate because they synchronize with it to avoid graphical tearing when the rendered frame is changed in the middle of a screen refresh. This was called V-sync on CRT monitors and while plasma and LCD screens don't have vertical retrace periods the same principle still stands - the image must be updated between refreshes.