Creation from nothing. The world produced by a wholly sufficient God with no pre-existing material. This is the formulation of later Jewish, Christian and Islamic theology, and it is not obviously the plain sense of the opening of Genesis, whose syntax permits either reading. Historians of doctrine generally date its explicit statement to the second-century CE arguments against Platonist and Gnostic accounts in which matter is eternal.
Ordering out of chaos. A pre-existing formless or watery mass is shaped into a world, frequently by the defeat of a monster embodying it. The Enuma Elish, in which Marduk kills Tiamat and forms sky and earth from the halves of her body, is the classic case; Hesiod's emergence of the ordered world from Chaos belongs here, as do a great many other traditions.
Creation by dismemberment. The world is made from the body of a slain or sacrificed primal being. Norse Ymir, from whose flesh the earth, whose blood the seas and whose skull the sky are made; the Vedic Purusha, sacrificed by the gods, from whose parts both the world and the social orders come; Chinese Pangu, whose body becomes the features of the landscape; and Tiamat again, which overlaps with the previous pattern.
The cosmic egg. The universe emerges from an egg that divides into heaven and earth. Attested in Indian material as Hiranyagarbha and Brahmanda, in Orphic Greek cosmogony, in Chinese, Finnish, Egyptian, Polynesian and other traditions.
The earth-diver. A being, usually an animal, dives beneath a primordial sea and brings up a small quantity of mud from which the earth grows. Distributed across northern Eurasia and North America, and one of the most striking instances of a narrative shared over an enormous area with no obvious mechanism of transmission.
Emergence. People, and sometimes the world itself, ascend into this world from previous worlds beneath it. Characteristic of Puebloan and other Native American traditions of the Southwest, and integrated with their ritual architecture and ceremonial calendar rather than being merely narrative.
These are types rather than boxes, and a great many traditions combine two or more of them without evident discomfort. Explanations for the distribution, diffusion from common sources, descent from a common ancestral stock of narrative, or the limited number of ways a story about origins can be constructed, have all been advanced, and none commands general agreement.