It does go orf, but for disposal porpoises you can tip a 5 litre can of old petrol into your van and it'll burn fine when diluted with all that nice smelly new fuel.....
The problem comes when you have a tank full of old fuel that has lost its go as with lawnmowers outboards etc etc.
Unless of course by "off" you mean bacterially off, which does not happen readily to petrol but can happen with diesel, a very common problem on boats, with the diesel bug clogging filters and blocking injectors...
The bug does not grow in the fuel itself but at the interface between the diesel and any water that has got into the tank in the presence of air, the water is usually condensation in the winter months. It is easily prevented by filling the tank to the brim when you intend to leave the engine unused for a few months.
This applies to diesel only, not petrol.
As said by several folks above, the petrol loses its abillity to be ignited by a spark due to the evaporation over time of the lighter parts of the fraction that goes into the petrol at the refinery.