I have a 1972 Super beetle and my bug wont stop dripping oil. Whats the worse that can happen if my bug keeps leaking oil?

Oil collects dirt, dirt collects on fins, fins do not cool as well, engine runs warm.
Clark

An oil leak will not repair itself, nor leak less. More than likely it will end up leaking more.

Aside from what Bluebug said, and a big oil stain in the driveway, whatever is leaking could leak much worse, and possibly lower the oil level in the engine to a critical state.

Air and oil are the only things cooling the engine. Less oil = less cooling. Less oil = less lubrication. Less cooling and lubrication = fried engine.

Until you repair the leak, make sure you check the oil level everytime before you drive it. Also check it every hour or so if you're driving a long distance. Carry extra oil and top it off when needed.

Pay attention to the oil light in the speedo. If it comes on or flickers, stop immediately and check the oil. If the light is on steady, it means you have NO OIL PRESSURE. If it flickers it means that the oil level/pressue is dangerously low, or the engine oil is extremely hot (loss of viscocity).

Best bet is to locate the leak and fix it. The most common areas to leak are the valve cover gaskets, the main seal, and the oil cooler grommets.

Believe it or not but the oil pressure idiot light in the speedo is just that, an idiot light. The pressure switch is set at about 5psi., so if you get that light while driving you are in trouble and have already done damage.
Clark