How many FPS is actually useful in video games?

Many gamers obsess about their FPS (frame per seconds). I was asked my opinion on the actual useful number of FPS (from a cognitive point a view) by pcgamer.com (here) and my answer made some of them snort into their coffee. I argued that the CPU/GPU resources usually allocated for displaying more than 24 FPS should rather be used for higher resolution (and smaller input lag). Thank you to Alex Wiltshire for this very good article.