The authors determine some gravitational effects in the classical and quantum massive scalar field theories near a point mass in the Einstein theory in three dimensions and near a particular spinning point mass in the topologically massive gravity. Classically, they find the expression, to a first-order approximation in the deficit angle of the conical spacetime, for the self-force acting on a scalar charge at rest. Within quantum field theory, they obtain the vacuum expectation value of the energy-momentum operator for a massive scalar field by determining the Euclidean Green function. They provide an explicit expression for the vacuum energy-momentum tensor to first order in the deficit angle for an arbitrary coupling parameter. Near a point mass in the Einstein theory, they calculate the gravitational force on a massive test particle due to the backreaction of the vacuum energy-momentum tensor. For the minimal and conformal couplings, they show that the gravitational force is always attractive. Near the particular spinning point mass in the topologically massive gravity, they can prove that the gravitational force is always attractive for a massless scalar field.