Extra Virgin Olive Oil does eventually go out of date and has a shelf life when unopened of around 24 months before it starts to go bad.
Once you open the bottle of extra virgin olive oil it's best to use it up within a month or two to prevent it from going bad and losing it's taste.
I cook enough to where I use a bottle of extra virgin olive oil within a month so it's never been a problem but I've used bottles of extra virgin olive oil that I've had for 2 years before and it was still good enough to use.
The olive oil being past it's expiration date is still safe to use for cooking with but the flavor of the food you use the olive oil for will not be as good as it would be if you had used fresher olive oil.