I recently picked up am 80's Bianchi of eBay, it was complete minus cables and some silly Cowhorn bars as it was going to be a fixie project. I got it home cabled it and put some proper bars and tape on and it looked ok. Tires were obviously old but they held air so I took it for a 5 mile plod and it rode sweet! happy days!
A few days later it was a lovely day so decided to ride it to the pub to meet up with a few mates for lunch. sitting in the pub garden admiring the tatty celeste paintwork in the glorious British sun (it does happen here from time to time lol) then suddenly and with out provocation Ptffffffffffffff from the front tire! I got up and moved the bike a few inches and Ptffffffff from the rear tire! I can only think sitting in direct sunlight (32 degrees C) upped the pressure to a point where the aged tires and tubes could not cope anymore.
Totally my own fault for not checking and assuming everything was good.. Nice 6 mile walk home and and I am still being ribbed about it now lol.