Is it illegal to own a video-game rated 18 if you are under 18 years of age

According to British law, (I'm not so sure about American) it is; as many will realise, illegal to buy a product rated above your age. However, nothing mentions the act of posessing these items. Therefore, you can have posession of them, but many will take the approach that this is with a parent's consent.
(see bbfc.co.uk)
However, due to a loophole that exists since the forming of the law (1984), this law cannot be lawfully imposed. It is not enforcable, nor a punishable offence.

I hope that will be helpful.