Positron trapping into vacancies in semiconductors is studied on the basis of Fermi's golden-rule calculations. The emphasis is put on the comparison of the trapping properties into defects in different charge states. In particular, the temperature dependences are investigated. Important features for vacancy-type defects in semiconductors are the localized electron states within the forbidden energy gap and (in the case of negatively charged defects) the weakly bound Rydberg states for positrons. Compared to vacancy-type defects in metals, these features make possible new kinds of trapping mechanisms with electron-hole and phonon excitations. For charged defects the Coulomb wave character of the delocalized positron states before trapping determines the amplitude of the wave function at the defect and thereby strongly affects the magnitude of the trapping rate. As a result, trapping into positively charged defects is effectively forbidden while negatively charged defects show remarkable properties which differ from the picture established for positron trapping in metals. The trapping rate into negative defects increases strongly with decreasing temperature and at very low temperatures ``gigantic'' values may result.