The two basic causes of aircraft tire blowouts are hot brakes and FOD like in the Concorde accident. Tires can also blow from under inflation heat buildup while taxiing. Some aircraft actually have a taxi distance limit after which you have to chock the wheels and let the tires cool off. This limit would normally only be reached if several runway changes occurred while taxiing.
The USAF lost a C-5 during an air refueling training mission when a tire blew quite a while after takeoff, and started a fire in the cargo compartment. It was determined that one of the brakes had been in full antiskid braking mode since initial taxi and thru takeoff. With 24 braked wheels and fairly light weight it is not really surprising that nobody noticed. Brake temp gauges were installed after this accident.
Joe