I have the same thing happening to me on my `95 Accord LX.
It never made this kind of noice before and I did check my brakes and they were like new. (I've heard that they last long in accords)
Maybe this helps....

Does the clicking noice sound when the gears are switched? (I have an automatic)
I was woried that this can be a trany problem but now atleast I know I'm not alone and can you guys also post if you have a MT or a AT. Althought this does not exclude a trany problem.

I will check my brake fluid reservoir.
Also, if anyone drives an accord somewhere in the years of 94 - 97, have you guys noticed your brake pedal kind of fall in when braking but at the same time you have new brakes and normal level braking fluid?

Thanks a lot I hope this helps someone somehow.
Vitalichka