@spendius,
Another classic example is when the offense commits a foul, but the play results in a turnover (fumble recovery or an interception by the defense). The defense will decline the penalty, let the play stand, and take possession of the ball as a result of the turnover.
Or... if there's a defensive penalty on a play that results in a touchdown. The offense will decline the penalty and keep the touchdown.
There are some exceptions but, in general, if the penalty is accepted then it's as if there was no play.