every time a person requests a page from my site, 
     the counter would give a satisfying 'Click!'

This is going to be a pretty loud night for the author ;)

I guess most people here know this site well, but if not it's definitely worth exploring. Lots of cool projects and much to learn.

I wonder what will happen if the frequency of requests is faster than the counter refresh rate. Does the counter stay consistent ?

It reacts to a pulse, so you could solve that with a queue in software, without that, my guess is that it would be missing clicks (pulses would overlap, since I'm assuming there is some minimum required width of it)

Suggested improvement: put a webcam in front of it for full-circle :)

Another nice electromechanical hit counter: https://vimeo.com/119746422

Hm, this seems like a pretty risky way to connect this device to your PC - using a serial port.

Edit: And THAT connection: http://meuk.spritesserver.nl/foto/foto/misc5/img_1999.jpg

He has discussion about that hack here: http://spritesmods.com/?art=mechctr&page=2

Seems reasonable enough to me.

Sure, depending on your computer. If you have a $500 graphics card plugged into a 600W power supply, connecting wires into ports that might short circuit could be seen as a 'bad idea'.