We formulate a new problem as Object Importance Estimation (OIE) in on-road driving videos, where the road users are considered as important objects if they have influence on the control decision of the ego-vehicle's driver. The importance of a road user depends on both its visual dynamics, e.g., appearance, motion and location, in the driving scene and the driving goal, e.g., the planned path, of the ego vehicle. We propose a novel framework that incorporates both visual model and goal representation to conduct OIE. To evaluate our framework, we collect an on-road driving dataset at traffic intersections in the real world and conduct human-labeled annotation of the important objects. Experimental results show that our goal-oriented method outperforms baselines and has much more improvement on the left-turn and right-turn scenarios. Furthermore, we explore the possibility of using object importance for driving control prediction and demonstrate that binary brake prediction can be improved with the information of object importance. * Work done during an internship at the Honda Research Institute, USA.