I never realised petrol went off, worryingly I've been topping up my stoves and lantern with fuel that must be 8 or 9 years old. Still burns okay
It's not so much that it goes off, rather that it looses it's octane rating over time.
For your run of the mill car it really makes very little difference, for forced induction high performance cars it can be fatal for the motor.
Many modern performance cars have a ECU that has active knock control, so if knock (what destroys many high performance petrol motors) is detected the ECU will automatically retard the timing.
The car may feel a bit more sluggish but other than that it should run ok unless the petrol has seriously deteriorated.
You could if your worried add octane boaster, some are better than others, but either way my choice would be to rotate petrol supplies regularly.
Our Smart car doesn't really care too much what petrol is added, my Supercharged MX5 is extremely sensitive to bad petrol, to the point where i can tell if a petrol station has had it's fuel standing in it's tanks for a while.
With the MX5 i always fill up at the busiest petrol stations that way you can edge your bets on it being fairly fresh petrol.
For diesel i honestly wouldn't worry too much, as said the only real worry is water collecting in the storage tank as this can set off a algae bloom that will cause running problems.
The main worry for diesel is that if your fill your container up in summer you will have a summer blend, this will cause problems if you decide to run it in the depths of winter.
For heaters, cookers etc that run on diesel there really is no worry.
We have a 5 ton diesel tank at our summer house that was last filled up 10 years ago, it still ran great this last winter.
Cheers
Mark