We examine the effects of nonradiative losses on lasing in crystalline and amorphous organic thin films. In crystalline films, the dominant loss mechanism is singlet-singlet annihilation, and this must be avoided if lasing is to be achieved at practical current densities. The electrically pumped crystalline-tetracene laser structure of Schon [Science 289, 599 (2000)] is studied in detail. Optical and electrical confinement in the bulk structure appears unable to explain the spectral narrowing reported; consequently, we consider electron-hole plasmas, self-focusing at interfaces, and crystal defects as possible sources of the reported phenomena. In amorphous films, lasers are likely to have to operate at current densities J<1000 A/cm(2) due to a combination of nonradiative losses. The performance of potential lasing materials is quantified by the external quantum efficiency-current-density product, eta(EXT)J. Electrically pumped lasers require eta(EXT)Jsimilar to5 A/cm(2); the best amorphous devices currently posses eta(EXT)Jsimilar to0.3 A/cm(2). However, we demonstrate that electrically pumped lasing in amorphous materials should be possible using indirect pumping techniques.