Chris's discussion of the role of technique was pretty darn good. I'd like to simplify (for once) a little to the following: In order to be a very good cook, you must have enough technique that technique itself becomes transparent. In other words, you can't make a competent holstein until you know how to cook a fried egg -- which you can't do until you know about preheating the pan, how to crack an egg, how to flip it, and so on.
Chalkdust's discussion of various cuisines takes a bite out of truth's behind, but I'd put it somewhat differently. Develop your skills and your palate by experimenting as widely as possible.
Learning to cook "French," (aka "fine dining") is a shortcut to a very powerful set of techniques because cuisine itself is so varied and inclusive; and the tradition of teaching the cuisine so well systematized. Otherwise, all the imperial cuisines (French, Chinese, American, etc.) include a lot of regional and colonial cuisines -- more or less equally. That makes them varied in their use of ingredients and techniques. They act as a kind of shortcut to world cooking. A cook with strong French technique is not going to have much trouble adapting to Chinese food -- and vice versa.
For God's sake, acquire some decent cutlery, learn to keep it sharp, and do keep it sharp. You don't need the "best" knives, but you do need sharp knives.
If there's one thing all good cooks know, it's how to cut an onion.
Knowing how to taste is hugely important. The most important thing? Maybe. Having an open mind and a palate trained to appreciate all sorts of things is part of it. Try and eat adventurously. Don't let the "idea" of foods, whether sea slugs, kidneys, chitlin's, or whatever put you off. You can't learn to taste until you get your preconceptions out of it.
Eat ethnic, eat diverse. When you take a date to dinner, the meal should be a pleasure and not a challenge. On the other hand, when you take yourself to lunch push yourself to try new things. Especially spicy things.
Read, read, read.
Read cookbooks. Read food magazines. If you're cooking at (or near) the professional level it's important to stay on top of trends. The easiest way to do it is by reading. Read top chefs and restaurants as much as possible. It's free to sit in a Barnes and Noble -- you can even take notes.
The internet is a huge help. Research the menus of top (by review, by Michelin rating, etc.) restaurants and see what they're serving. This is especially helpful for staying current on ingredient combinations. Learn to track the differences between what's happening in Paris, the rest of France and Europe, the east and west coasts, the heartland, and so on.