What determines if a joint should be recaulked? Should old caulk always be removed?

If the old caulk is cracking or pulling away from the surface, dig it out and replace it. Prime the bare wood then re-caulk. Any butt joint in siding or other joints between two pieces of wood should be caulked. You DO NOT want to caulk the lap joints of siding since they allow moisture to get out from behind the wood.