"Mommy, where do little orcs come from?"
Well, where do they come? Birthed from the earth like Uruk Hai? Or was Aristotle right - "some spring from parent animals according to their kind, whilst others grow spontaneously and not from kindred stock"?
Roll a d6, or just pick one of the following:
1) Divine Origin - The monster is born from a god or goddess, or from some embodiment of evil (i.e. The Devil.) It might originate from a mortal being granted divine powers. This especially suits unique monsters, like Jormungandr, or ones in limited supply, like the three gorgons or the three hekatonheires. Such creatures may be sent to the mortal world as a punishment for themselves, or as a punishment to mortals, or both. Divine curses also fall under this - a mortal turned into a monster (full or part time) generally is so because some god is angry at him or her.
Many monsters of myth originate this way - the various monsters of the Greek myths are the children of gods and goddesses or of gods and mortals. The two great monsters of the Norse mythos, Fenrir and Jormungandr, are the sons of Loki and a giantess.
2) Spontaneous Generation - The monsters appear from source material without any parents. Some may spring from corpses, or appear from magical fluxes or botched spells, or from pools of darkness touched by human fears or desires. They may appear from the clay of the earth touched by the sun or the rays of the moon. Or perhaps they simply break out of the rock, one after the other, leaving tunnel-like birthing tubes behind them.
The originating substance and the "catalyst" event or substance would determine the final monster. Perhaps orcs come from darkness touched by hate, but gnolls by the animal fears of mules and dogs dragged into the underworld by intrepid adventurers.
3) Evolution - The monsters have evolved in the usual Darwinian way, filling some niche in the natural order. Because of the unusual nature of fantasy worlds, the niches they fill may be quite unusual - cleaning out dungeon passages, eating rust, devouring sources of magic (toxic or otherwise).
Weird crossbreeds are covered here - the bewildering hydra/manticore/chimera/gorgon/etc. melting pot of late 1st edition AD&D is a good example of "what if X and Y mated, what would Z look like?" The tarasque is one of these - born of two other monsters.
4) Mutation - The monster is a mutation of some other creature. The original creature has its own origin, but this one is a mutation of that being. This can be from direct magical exposure, the "radiation" of some cosmic good or evil, or from the holy or unholy energies of a sanctified place. Mutations may result from using too much black magic, or from dabbling in secrets Monster Was Not Meant To Know. They may be a spontaneous mutation, due to unique circumstances (like the Elfquest Madcoil) or normal sexual reproduction under bad circumstances (born under the light of a blood-red moon, perhaps).
This can also cover possession - a demonic (or otherwise) being taking over, and in the processes, warping, an animal, human, or monster. If a species originates this way, its offspring may or may not be equally mutated and monstrous.
5) Magical Experimentation or Creation - The monster may be created by a wizard, like a golem, or the result of some strange experimentation, like the dreaded owlbear. This may be a one-time event, which must be repeated each time you want one, or they may breed true after being released into the wild. The origin materials may be common - stone for a stone golem, or extremely precious, like dragon eggs for draconians.
Evil humanoids boiled up out of experimental vats of flesh or dug out of the clay of the earth after use of strange rituals are generally covered by this background.
6) Another dimension - The monsters may simply come from "somewhere else." They may appear when the stars are right, port in from the Dungeon Dimensions, be summoned from the elemental worlds by foolish wizards, or unleashed when the gates to hell are broken. Once arrived on the mortal plane, they may be stuck, desperate to flee, or desperate to stay (especially if they like to feed!)
If they come from the mortal realms originally, and were banished to "somewhere else," check again to see what their origin was (generally, Divine Origin does well as a default).
Note: The important thing about origin is that it should spark some interest in the monster, and help determine the kind of actions it might take and the way it might operate. Consider it (and any other "ecology" element) as an adventure hook. If it doesn't provide a hook, it's not especially useful. Consider the owlbear - possibly the result of a mad wizard's experiment. Okay, now I want to meet that wizard (and I'm scared to meet his other experiments.) Or orcs - is it better that they are mundane creatures and breed like rabbits, or if they are fear-spawned solidified darkness with a purely malign raison de etre? Both provide hooks, so both are useful to the GM, and to the players. "If they are natural, maybe we can find out what they want and negotiate with them" or "if they're spawned from darkness, I have a great idea how we can use that Light spell next session . . . "