After driving and then turning my car off there's a "clicking" noise that lingers. It's a single click every 20 seconds or so. Popped the hood and the valve cover looks greasier than usual. Any thoughts?

 

Sure it isn't just the sound of metal cooling? If you are convinced it isn't, hit the lock button and see if it stops. My old pickemup cooling down was very rhythmic, could stand in for Coltrane's drummer.

 

Thats what I was thinking. If the valve cover seems greasy you may want to address that issue. Could be a leaking valve cover gasket or something else. I would clean it well and find the source and repair it.

Besides heat I can't think of anything that would really cause a clicking.