Before I started driving my dad made sure I knew how to do a few things and I believe that everyone should have these skills.
1. Check your own oil and other fluids and be able to refill them if needed. I don't mean that you need to know how to change your oil and bleed your brakes (although it wouldn't hurt to know that too) but you shouldn't need to rely on a guy for something like checking or refilling your oil. You should also know what kind of oil to get for your car.
2. Change a flat tire. Obviously, there will not always be someone to do it for you and you won't always be able to have AAA come do it for you. It's not very hard just requires a little muscle. I use my legs to tighten and loosen the lug nuts. It works until you can get some where and use a pneumatic torque wrench (you should also know what that means if you don't already. It's the really loud wrench they use at Good Year to loosen the lug nuts on your car. It's hooked up to an air compressor and makes sure all the lug nuts are properly tightened and your wheel won't fall off, cuz that would be a bummer). Also know that the spare tire is not the same thing as a regular tire. Most spares or "donuts" are much much smaller and not meant to be driven on for long periods of time.
3. How to check tire pressure and put air in a tire. Always keep a tire pressure gauge in your "emergency car kit". You should also know how much air should be in your tired. This is indicated on door panel where the door latch is and in the car manual. Most cars are around 32 psi.
4. Know how to use jumper cables and keep them in your car. Write down the following steps and keep them in the car: 1st attach the red clamp to the positive terminal (usually has red paint on it but always has a plus sign) of the dead battery 2nd attach the red clamp to the positive terminal of the live battery 3rd attach the black clamp to the negative terminal to the live battery 4th attach the black clamp to the negative terminal on your car 5th start your car 6th remove the clamps in reverse order
5. Know how to steer out of a skid by steering into the skid. Sounds counter intuitive doesn't it? But it's true. If you hit a patch of water or ice and start skidding turn INTO the skin, not out of it. DO NOT slam on the breaks! Keep your foot on the accelerator and let off the pressure just a little. Then, if you are skidding to the right (clockwise) very gently turn the steering wheel to the left. Do not jerk the wheel, gentle fluid motions. I have also been told that you can just let go of the steering wheel entirely and the car will straighten itself out but that idea totally freaks me out so I don't do that.
Well, that's my Southern Soapbox. If there's anything else you think of to add to the list let me know in the comments and I will add it to the list!