It's fine to be a world-class flat fixer, but it's better not to puncture at all. This quick checklist before you leave the house can make a puncture less likely -- and quicker to fix if it does happen.
Check your tires. Very few punctures happen the instant you ride over something (pinch flats excepted). Usually, a small and sharp shard sticks in the tread, then works though to the tube during many wheel revolutions.
Find these bad boys by checking the tread in bright sunlight or with a flashlight. If you spot something, carefully pop it out (not into your eye) with the corner of a small screwdriver. Dig a little to made sure you don't leave the sharp tip.
While doing this, look for thin areas where the casing is beginning to show through the tread. Never continue to ride a worn tire. It's a lot more susceptible to punctures. A front flat can make it hard to keep the bike upright.
Check your seat bag. It should be well stocked with two tubes, two or three tire levers and a patch kit. Don't forget a small piece of Tyvek, duct tape or other strong, thin material that's suitable for lining ("booting") the inside of a cut in the tread or sidewall.
Put each tube in a zip-shut plastic freezer bag. They'll be easier to pack than in a box, and less likely to have holes worn by rubbing against tools. Sprinkle talcum powder into the bags as another way to reduce friction. It'll make the tubes easier to install, too, and it might even reduce the chance of flats.
By the way, do you have the right size tubes? We've seen riders flat on their 700C tires and pull a 26-inch mountain bike tube out of their seat bag. Or, riders on fancy wheels with deep V-shape rims will have useless tubes with standard-length valve stems.