My list (i don't include gassing up because. . well that's just obvious!):
1) change the tire (including knowing to rotate the tires at least twice a year and knowing to never put a non-fullsized spare on the drive wheels)
2) How to recognize common mechanical problems. Some mechanics love to try to take advantage of women because they assume the woman won't know squat about cars. If you can diagnose problems, you'll avoid being suckered in. My girlfriend's valve cover gasket was leaking. She took it into the shop to get it replaced (I was 600 miles away at the time or I'd have done it for her). Guy tried to tell her she had a cracked head and would need to pay over a grand to get the job done. She proceeded to tell him in intimate detail where the leak was, why it leaked, and how to fix it, just before taking the car to another shop
3) Location of all the fluid checks, and what to look for when you check them. i.e. if the oil's full that's great, but if it's the color of chocolate milk you have a blown headgasket and need to get it fixed before you wreck the rest of your engine
Those are the real basics. Beyond that, it's not a bad idea to learn:
4) how to fix stuff. If your alternator dies you can pay someone $300 to fix it or you can fix it yourself with a $30 part and half an hour. Knowing how to work on her car has saved my girlfriend a tow bill or three, 'cause she just fixed the problem out in the field.
5) How to drive. Learn to REALLY drive, not that BS they teach you in driving school. Learn spin avoidance, steering with the throttle, and how to control your car at the limits of its performance. Sure, you'll probably never race it, but if you have to swerve suddenly on an icy road, you'll be using the same techniques as you use controlling it at the limits on dry pavement.