If you just finished your caulking job and have some leftover in the tube, cap off the cartridge with a long nail or screw. Simply insert the nail or screw into the open tip. Once the nail is inserted wrap duct tape around it and the tip of the tube to make sure that air does not get in and harden the caulk.
A used tube of caulk can also be unplugged with a screw. Take the tube and cut off the nozzle end so that the hole is slightly larger than the first cut. Then drive the screw into the nozzle end of the hardened caulk and use the screw to pull out the hardened caulk. A screw with course threads such as deck screw will work the best.