Originally Posted by dwinks
Wider, lower-pressure tires, all other factors being equal, will get far less flats than narrower, higher-pressure tires. A flat occurs when an object is pressed against the tire with greater force than the tire is able to withstand. Wider, lower-pressure tires will be able to deflect more when running over an object, exerting less force downward upon whatever you ride over (as there's more area supporting your weight, so less weight per area). Often the downward force is less than the amount of force required to push said object through the tire, and you simply roll over the object and continue on your way. If you ride narrower tires, they require higher pressure, and thus have more weight per area pressing down, which greatly increases the chances of pressing down on an object with enough force to push it through the tread.
Contrary to what some of the above posters claim, your weight absolutely has everything to do with getting flats. For an example, imagine pushing your bike, without any panniers or anything else weighing it down, over a huge field of super sharp glass. Since there's almost no weight pressing down on the tires, it's fairly reasonable to expect the bike to suffer no flats from this. Now hop on and ride over the glass. It would be very reasonable to expect a flat in short order due to the weight on the tires pressing down onto the glass. An unloaded biking being one extreme and a loaded bike with a clyde being the other. A lightly loaded bike with a lightweight riding would be somewhere in the middle, and with the same bike, same tires, same conditions, the lighter rider would have far fewer flats.
Assuming you don't buy some 1000+ gram POS tires, wider tires don't even slow you down, as the wider tires have LESS rolling resistance than narrow, an extremely negligible increase in air resistance, and decreased suspension losses (energy/speed lost to 'road buzz' and other vibration, which is a huge factor in speed). Narrow tires have a weight advantage, which outside of extremely competitive (think constant attacking) riding, means absolutely nothing, and for the average rider, the lower suspension losses of a wider tire far outweigh the penalty from slightly higher rotational inertia. So overall, wider = faster, provided your wider tire is a quality tire, and not some $12 POS knobby from Wallyworld.
Not only do you get a very noticeable decrease in flats with wider tires (especially if you're a clyde), an increase in speed in 99% of riding situations, but wider tires are just more comfortable and safer. Basically a win-win-win.
Slap the widest tires on there you can fit, with moderate flat prevention (don't go overboard on flat prevention tires, or they'll be dog-slow), and you should see a drop in flats. Even if you get tires with the exact same tread thickness, construction, etc as the ones you have now, but simply wider and lower pressure, you'll get noticeably less flats. The key is keeping the PSI low, as higher PSI does nothing other than make the ride slower, less comfortable and much more likely to hammer debris through the tire rather than deflecting and rolling over it.
I've had pretty good luck with Michelin City tires with "ProTek" myself. One flat in the last 4,000 miles, which was from a large, pyramid shaped chunk of glass on a rainy day. Had it been dry, it probably wouldn't have flatted even on that, but the water lubricates the glass, dramatically increasing the chances of it penetrating the tire.