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I agree with Squaredisk and Jonny 69.
I never go out of walking distance from home without puncture repair kit. The same with a car, I make sure I can change a wheel - and that means having a tool that will undo wheel nuts that have been tightened with a pneumatic spanner.
Since J B Dunlop suffered his first puncture in 1888 there have been attempts to make puncture proof tyres, but none have really been successful. So far as bikes are concerned, it's possible to have tyres that are resistant to puncturing, but these are usually so heavy that there's little pleasure to be had using them.
If you want any measure of speed you have to accept the risk. It's a good strategy to consider the conditions for the ride that you intend to do - a wet winter clubrun needs tough tyres and plenty of spares, a 25 mile TT on a good dry road, if you're in good form, needs the lightest tyre you can afford.
Incidentally, I've just recovered my best TT wheels from a shed where they had been quietly rotting away for about the past 25 years. I'm not planning to use them, I just couldn't bear seeing them decompose. The front tub is a Clement silk (about 7 or 8 ounces, say 225 grams), and it seems still to be in useable condition. It's done enough miles to wear away the centre tread (admittedly very fine ) but there are no cuts at all.
Of course, it's only ever been used in the dry!
This is the best I've managed.
Avoiding fragile tyres or tyres with a sticky tread which picks up debris is a good start (especially the latter). But the flipside to this is the roads around here are in dreadful condition, there's always sharp flinty stuff as a result and there's always broken glass. You can't avoid it all, so you might as well go out prepared.