One thing that hasn't been mentioned. Once in a blue moon, you'll get something, usually glass, stuck down a hole or cut in the tyre. With the tube out, you don't feel anything inside the tyre but with the pressure of riding, it pokes out and rubs a hole in your tube. A rare one but frustrating - again, it's good to check where the punctures are happening and look for a common origin. If there is a common origin, look for a cut in the tyre and go probing (I use the corkscrew on my pocket knife).

Old tyres, either old in age or just worn, will puncture more easily - most punctures occur in the last 30% of a tyre's life according to some websites. New tyres are relatively cheap and always fit new tubes with the tyre.
Modern tubes are rubbish and I've had them start to leak or pull away from the valve just through age. I'm not talking years either, an Aussie summer is enough to render your spare tube suspect.

If you're picking up thorns on the bike path, an old trick that works is to drape a bit of light electrical wire over the tyre and tie it to the fork so the wire drags lightly on the tyre. The idea is that you pick up the thorn and in half a revolution the wire flicks off the thorn. It works (I needed it on one commute some years ago). You can also buy a commercial version of the same thing.

One last point. If you're using the wrong swear words during the repair, the puncture fairies will get grumpy and target you. These swear words are specific to your area so we can't give you a list (besides, they're secret)