The possibility of removing a dangerous asteroid from collisions with the Earth using the kinetic method in combination with the effect of gravitational maneuver to reduce the required change in the asteroid’s velocity is discussed. The asteroids Apophis, 2000 SG344, 2008 UB7, 2006 QV89, 2008 EX5 are considered as examples. For these asteroids, we found possible collisions (including previously unknown ones) and approaches to the Earth preceding these collisions. It can be noted that in many cases the approaches on the trajectories leading to collisions are closer than on the nominal trajectories. In the case of close approaches, the effect of the gravitational maneuver can reach several orders of magnitude. The corresponding estimates are given. With the advance impact on a dangerous object by the kinetic method, in many cases, in principle, it is possible to withdraw the asteroid from the impact with the Earth using the capabilities of modern space technology. Estimates of the probability of collision of a number of dangerous asteroids with the Earth, the Moon and planets of the Solar system, obtained by numerical modeling using the Monte Carlo method, are also given. In most cases, only collisions with the Earth and Moon occur for selected asteroids. In addition, the probabilities of rendezvous with the Moon and planets at 10 and 100 of their radii are estimated.