There are three major classes of insect genetic systems: those with diploid males (diplodiploidy), those with effectively haploid males (haplodiploidy), and those without males (thelytoky). Mixed systems, involving cyclic or facultative switching between thelytoky and either of the other systems, also occur. I present a classification of the genetic systems of insects and estimate the number of evolutionary transitions between them that have occurred. Obligate thelytoky has arisen from each of the other systems, and there is evidence that over 900 such origins have occurred. The number of origins of facultative thelytoky and the number of reversions from obligate thelytoky to facultative and cyclic thelytoky are difficult to estimate. The other transitions are few in number: five origins of cyclic thelytoky, eight origins of obligate haplodiploidy (including paternal genome elimination), the strange case of Micromalthus, and the two reversions from haplodiploidy to diplodiploidy in scale insects. Available evidence tends to support W.D. Hamilton's hypothesis that maternally transmitted endosymbionts have been involved in the origins of haplodiploidy. Bizarre systems of extrazygotic inheritance in Sternorrhyncha are not easily accommodated into any existing classification of genetic systems.