Inner tubes puncture for two reasons: either a sharp object penetrated the tire or worked its way between tube and tire, or the wheel "bottomed out" and the tube got pinched between rim and tire. The latter usually causes a pair of telltale "snakebite" punctures.
Punctures caused by sharp objects such as nails, wires broken off from street-cleaning machines, and glass can almost always be prevented with a Kevlar tire liner. At this point I used to recommend ``Mr. Tuffy's'', but recent experiences have shown that they cause way more flats than they prevent because the hard edges rub against the tube until it blows out. No amount of sanding and melting with a lighter has fixed this. They used to have a soft version that worked well, but the current version, recognizable by the black stripe, is dangerous. Don't buy! If you must use them, cut the end straight off and only soften the corners a bit; don't cut a long soft curve because it's the sides that eat into the tube. There is a ``green slime'' brand that spares the tube, but it's a little on the soft side and lets some debris pass, and only lasts a year or two before it falls to pieces. Still seems to be the best bet right now (2004).
Snakebites are caused when hitting an obstacle such as a pothole hard so the inner tube gets pinched between the rim and the obstacle. Tire liners help very little here. The best prevention is to inflate the tube to exactly the pressure printed on the side of the tire at all times, and rechecking the pressure at least every other week because butyl inner tubes leak air. Latex tubes are nearly puncture-proof but leak air at a frightening rate.
Do not use light-weight tubes. Some of them weigh 60 grams or less, but are very prone to punctures. If you use tire liners, occasionally check for pieces of glass that became lodged in the tire; they can work their way into the tire if left in long enough. Look as if you knew what you are doing when cutting away at your tire with a knife point. Do not use ``Wrench Force'' tubes, they have inferior valves that break easily when installing.
See also an article on "Repairing Punctures"
