[en] We explicitly construct normalized solutions of the Klein-Gordon equation for various types of attractive potentials. Our computed binding energies of several short- and long-range potentials are compared with results published by different authors. Special emphasis is laid on the determination of critical potential strengths, i.e. the onset of spontaneous pair creation of spin-0 particles. In the vicinity of these critical values the single-particle interpretation breaks down. The phenomenon of simultaneous particle and antiparticle binding in a short-range potential is investigated. (orig.)