This has bugged me for centuries. How does a nail, which I can only assume was lying flat on the tarmac at the time, puncture a tyre at 90 degrees like someone took a hammer and nailed it there?
It bugged the Romans for centuries too, until they realized that chariots did not have pneumatic tires.
I can think of two things that could cause the nail to move into a position to punture the tire. First is the impact of the tire into the nail, and the second is the nail getting caught between the tread blocks of the tire. Either could cause the nail to move. Once the nail is in position, the weight of the car is the hammer.
I work in tyres, and as you would expect see this quite often, they also aren’t normally in straight but usually within 10 degrees of it. I’ve never thought about why it happens, just been glad that it does 
If I had to guess I would come up with this. A car in front of you, or your front tyres flick the nail up and you just happen to run over nail at the wrong time. It does sound unlikely but think about how often you get punctures. Also people who drive in construction sites are more likely to run over a screw and stand it up for the next guy to run over.
I will also bring up that a tyre deforms as it hits the ground, so that may help the nail.
On a more helpful advice/usueless knowledge side of things, we see a lot more punctures in tyres with less tread, probably from the fact there is less tread to cushion the steel belt.
Don’t drive on a tyre with a puncture, especially if its gone flat. You will ruin the tyre if you drive far enough on it. (50m along the highway on a flat tyre makes it irrepairable more often than not.)
Also, if whatever has punctured has gone through at an angle and can rub on the sidewall you will likely damage the sidewall and take it from being a repairable tyre to a throw away.
Hah, ya gotta love google, Romans and nails and the google ad is The Second Coming.
Anyhow, thanks Dag and cooky for the replies so far.
Could be that only the nails within ten degrees or so of perpendicular penetrate the tyre. Any more than this and they are just deflected. That’s why you only see this kind of puncture. How they get in that position is another matter.
I believe we’ve had this question before, and IIRC nails are almost always in the rear tire. This happens because the front tire runs over the nair first causing it to stand up a bit and the back one runs over the point.
I still want to know how my mom wound up with one in her sidewall.
Now let’s see if we can’t find that thread.
As a valet driver who often assists in helping customers change flat tires, I’ve noticed that most often the nail flattens the powered wheel: front wheel driven cars get the flats up front, and the rear wheel driven cars end up with the nails and screws in the rear tires.
Not a hard and fast rule, but that’s the trend I see most often.
Perhaps torque has something to do with it.
I’ve been thinking about this a bit more, and I like Dag’s idea of the nail being caught in the tread blocks. If it ges caught right, centrifrugal or centripedal (I can’t remember which) will cause the nail to start to fly out just as it comes to ground again.
Bingo 10 degrees is the norm, but maybe 10% or so are at the 45-90 degree mark, 80 or so degrees does happen, but normally limits itself to sticking in the tread, so I don’t think you can really consider that a puncture.
As for punctured sidewalls, it is rarer, but keep in mind when you corner that the sidewall of your tyres flexes quite a bit, and on say a hard left hand turn, your front right tyre would fold over a bit, bring the sidewall closer to the ground making it easier to puncture.