First suspect should always be to check your crank bolts, because they are most expensive and damaging if out of spec. Otherwise, most commonly in my experience that click has been the spd cleat. Grease the cleat(unless you are on a sandy area, dirt doesnt matter so much) and see if it goes away. Yes that means you wont be able to walk on your beige carpet but we cant have everything.
On flat pedals, sometimes the cage can even come lose.