For the Cauchy problem for three-dimensional compressible Euler equations, the authors study the effect of damping on the large-time behavior of solutions. First, the Cauchy problem is reformulated as a symmetric hyperbolic system with positive density. Then the authors prove a local existence theorem and establish the finite speed of perturbation propagation. Using effective energy estimates, it is shown that the damping prevents the development of singularities of a small-amplitude classical solution. The full solution relaxes in the maximum norm to the constant background state at a rate of \(t^{-3/2}\). While the fluid vorticity decays to zero exponentially fast in time, the full solution, in general, does not decay exponentially. Finally, the authors obtain some differential inequalities which demonstrate that solutions may blow up in finite time if the data is sufficiently large.