just like getting soaked, a puncture is a rare event that’s nevertheless very annoying. The best prevention is to use puncture-resistant tyres. These have layers under the tread that prevent bits of glass and the like from getting through to the inner tube.
The best puncture-proof tyres for commuting use — such as the highly-rated Schwalbe Marathon Plus — practically eliminate punctures.
You can also protect yourself by simply looking where you’re going. Ride around patches of broken glass, not through them, and avoid sharp-edged potholes that can cause a puncture by pinching the tube between tyre and rim. Fair-weather riders will find they get hardly any punctures anyway.
Dry rubber is fairly tough stuff, but water on the road acts like a cutting lubricant and helps a shard of glass get through the tyre. It’s not that punctures are just more inconvenient and annoying when it’s raining, they’re also more likely!