Whilst traveling to the excellent Interlink Expo in Milton Keynes yesterday, I saw a man trying to measure and photograph a pot hole on the A421. My guess is, he has suffered some damage and possibly lost a tyre due to hitting this pot hole.
In my business, I regularly speak to people who have suffered at least 1 burst tyre (and sometimes 2!) as a direct result of driving over a deep hole in the road. I am often asked if I could offer any suggestions to help prevent this. By keeping tyres at the correct pressure you have the best chance of avoiding a problem. Tyres under or over inflated are at a greater risk of this type of impact damage. Something else to be aware of when choosing a car, lower profile (skinny) tyres will be more susceptible to damage as they provide less absorption to impacts.
Finally, if you do hit a pot hole or any other object including kerbs, have a quick check round your tyres for any obvious damage including bulges in the tyre (like an egg) and if you find anything, get some advice from a tyre expert because the tyre may be structurally damaged and dangerous.