Have you ever wondered, as you're running a world full of fantastic creatures, how all those mythical and imaginary beasts came to be? I'm not talking about how the game authors thought of them or what inspired them, but of their origins within the context of the game world. Sure, some of them might be the products of a mad wizard's experiments, but that's a stock answer overused to the point of cliche.
My question is, why couldn't some or most of the purely imaginary D&D menagerie (at least the ones that are truly living, not constructs or undead) have evolved naturally within the game world? In the real world, convergent evolution has produced mammals (and in the past, reptiles) that look like fish, and mammals (and in the past, reptiles) that can fly like birds. There are creatures that can can generate electricity as a defensive weapon, animals with built-in body armor, prehensile noses, color-changing skin, bioluminescence, crazy egg-laying mammals with bird-like beaks...
(I'm looking at YOU, Mr. Owlbear, fictitious-but-entirely-plausible cousin of the duckbill platypus!)
If the real world can produce an electric eel, why couldn't a world in which magic is every bit as real as electricity produce a basilisk or a blink dog without the intervention of a god or wizard? If the real world can produce creatures that secrete paralytic chemicals, in a world where alchemy is real, why not one that secretes a substance that corrodes metal?
Even the mythical hybrids like griffons, hippogriffs, and manticores could be the products of fantastic evolution, if we take them a little less literally, i.e. a griffon has parts that resemble those of an eagle and a lion, rather than literally being half eagle and half lion. Oddly enough, one thing our real world evolutionary processes never seemed to produce is a vertebrate with more than four limbs, but I don't know of any sound scientific reason why such a thing couldn't have happened in a parallel reality. Could all those critters with four legs and wings be members of the same fantasy classification? Maybe dragons and griffons share a common ancestor.
Is a stirge a mammal or a bird or something else? Are lizard men descended from some species of dinosaur, or from a true lizard? Are they related to troglodytes? Is the four-limbed wyvern akin even distantly to the six-limbed dragon? All of this probably has little or no relevance to the game itself, unless you have players who make it a point to learn the primeval origins of fantasy species, but it's fun to think about.