We investigate the kinetics of generic single-species reaction processes when the reactants move ballistically, namely ballistic annihilation, A + A --> 0, and a ballistic aggregation process which mimics traffic flow on a single-lane roadway. For ballistic annihilation, dimensional analysis shows that the concentration and root means square velocity decay as c similar to l(-alpha) and upsilon similar to l(-beta), respectively, with alpha + beta = 1 in any spatial dimension. Analysis of the Boltzmann equation for the evolution of the velocity distribution predicts alpha = (2 + 2 mu)/(3 + 2 mu) and beta = 1/(3 + 2 mu) for an initial velocity distribution P(upsilon,t=0) similar to upsilon(mu) as upsilon --> 0. New phenomena associated with discrete initial velocity distributions and with mixed ballistic and diffusive reactant motion are also discussed. In the aggregation process, each "car" moves at its initial velocity until the preceding car or cluster is overtaken after which the incident car assumes the velocity of the cluster which it has just joined. For P-0(upsilon) similar to upsilon(mu) as upsilon --> 0, the average cluster size grows as n similar to t((mu+1)/(mu+2)) and the average velocity decays as upsilon similar to t(-1/(mu+2)). We also derive an asymptotic expression for the joint distribution function for the cluster mass and velocity.