I think there are two basic camps among cooks. Those who follow a recipe to the letter and those who consider a recipe more as a general guideline. I most definitely fall into the second camp.
I love collecting recipes, I have tons of them on my computer, stashed in a pile by the desk, and heaped with the cookbooks on the bookshelf. But I also have a short attention span for them... I tend to read through quickly, get the gist of it, and start cooking. If I don't have one of the ingredients or not quite the amount it calls for, eh, I'll improvise. One of my favorite things is to find an ingredient and build a recipe around it (much like the osso bucco experiment). If it's something I haven't cooked before, I'll do a little research on-line or in my cookbooks first and see how it is usually prepared, see what I have on hand or what sounds good, and get crackin'.
A few exceptions to the above:
First, baking. Baking, probably more than any other type of cooking, can be a very exact science. I have had very little luck improvising with baking, though I am working on getting a better understanding of ratios and other science-y stuff to improve my chances. This printable PDF on Cookie Science is an excellent reference tool, and is based on Alton Brown's show Good Eats, which I love. You want to know about how something cooks or why a particular technique works? Ask him, he knows.
Second, and I hate to admit it, but read the whole recipe first. Start to end. Seriously. Unless you've done it before and you know what to expect, read through the recipe at least once. I've learned the hard way on this one and have gotten halfway through a recipe to discover I can't continue because step three requires the dough to rest overnight or the meat to marinate for 4 hours or some such. Not so great when you're making dinner and it's 6:30pm :P "Honey! How does pizza sound tonight?"
There is a bit of risk involved, of course... what you improvise may, quite frankly, come out awful. But, that's part of how you learn. Usually though, you will get a result ranging somewhere between "Eh, it's not bad" to "Ohmygod what's in this? It's amazing!".
So for those who fear cooking without a recipe or get stressed out when you don't follow the recipe exactly, loosen up a bit. Estimate how much a half a cup is in the palm of your hand; if you don't have the particular spice it calls for, try something else; see how that sauce comes out with a splash of sherry thrown in at the end. The more improvisation and experimentation you do, the more comfortable and confident you will become in the kitchen, as well as less dependent on tools and recipes, allowing you to explore even more. After all, whatever is on your plate right now only exists because someone once thought "I wonder what that would taste like if I cooked it...?" ;)