Like the armadillos, many decent tyres now include kevlar to reduce the probability of flatting. They seem to work pretty well, although they are understandably a little heavier than those without the kevlar. Although the armadillos may have been one of the pioneers of this technology, I'm not sure that they are much different from the competition these days.

One of the leading causes of flats, no matter what tyre you are using, is low tyre pressure. Most novices rarely check their tyre pressure and don't own a pump that can measure it, and subsequently often end up riding tyres at less than half the recommended pressure. This results in taking more effort to pedal the bike and a MUCH greater likelihood of getting a flat (although it does give a cushier ride). Upon checking your tyre pressure for the first time, you'll probably be surprised by how hard your tyres should be.

Therefore, my tip of the day to avoid flats is to buy a floor pump to keep at home that has a pressure gauge on it, and regularly (maybe once per month or two months) check that the tyre pressure is in the range recommended on the sidewall of your tyre.