The asteroids are a major source of potential impactors on the Earth today. It has long been assumed that the giant planet Jupiter acts as a shield, significantly lowering the impact rate on the Earth from both cometary and asteroidal bodies. Such shielding, it is claimed, enabled the development and evolution of life in a collisional environment, which is not overly hostile. The reduced frequency of impacts, and of related mass extinctions, would have allowed life the time to thrive, where it would otherwise have been suppressed. However, in the past, little work has been carried out to examine the validity of this idea. In the first of several papers, we examine the degree to which the impact risk resulting from a population representative of the asteroids is enhanced or reduced by the presence of a giant planet, in an attempt to understand fully the impact regime under which life on Earth developed. Our results show that the situation is far less clear cut that has previously been assumed, that is, the presence of a giant planet can act to enhance the impact rate of asteroids on the Earth significantly.