I have been lucky enough not to have bad encounters whilst using old tyres on my bikes, however:
A year ago I was driving home a 1980 Buick LeSabre I had bought from London, it had 4x old tyres from 25+ years ago (had been in storage since '90), and one of the tyres blew on the motorway. Thankfully there was the original spare, with probably the original tyre on that too. But because it is kept in the boot it is still maluable like from new. However, thankfully I didn't even feel the blow out, I was just looking for a helicopter
My Peugeot 205 also has a spare however it is kept under the car in a rack. I had that tyre changed one day and the tyre split whilst in the machine.. The tyre was dated 1991 and could have even been an original that came with the car.