There are a lot of takes on monsters and myth in books, TV shows, and everywhere else in pop culture. I recently read the Twilight series, with its very different (though still somewhat familiar) take on supernatural beasties. Every game and game world has to pick through myths, legends, and other game systems’ takes on the creatures of legend. Every GM then has the option to adjust monsters to match their own preferences– including familiar twists from family legend, a specific version of the tale told to you young, or just to change things to match a specific world or vision. I still reflexively imagine orcs as pig faced, thanks to the 1e Monster Manual.
If you grew up on tales of redcaps  (perhaps at your Scotish grandmother’s knee), you might alter your world’s redcaps to match those of your upbringing– throwing an interesting curve at your players and requiring investigation when they turn out different from the book version of the critters.
For example, Vampires
How many ways have vampires been presented recently? Vampires are all the rage, but who wants to be an undead bloodsucker? Under most of the myths, it’s no picnic, but in some worlds, there aren’t many drawbacks to unlife at all. It all depends on which world you inhabit…
Count Strahd von Zarovich  was the star of Ravenloft, a very popular AD&D module; later he became a big cheese of the demi-plane of dread. Strahd was similar to generic D&D vampires, but was altered in several ways due to his longevity and command of his realm. As “owner” of the whole realm, Strahd didn’t need to be invited into any building, unlike his lesser peers. Having lived with his condition for so long, he had prepared well to compensate for the few weaknesses of his condition and emphasize his already considerable strengths.
Forever Knight  was a late night TV show in the early 90s. From the body of vampire myths, the writers selected interesting weaknesses and strengths that often matched the mythical norm– but not always. Nick Knight was prone to getting lost in flashbacks, would “implode” if caught by the sun, and would be paralyzed (but not killed) when stabbed with a stake. Nick’s whole quest for redemption was a new lens on the traditional vampire as a remorseless killer.
White Wolf put out two lines of books, each starring vampires. In Vampire: the Masquerade , vampires had several common flaws and strengths, with a point buy system that made any given vampire tremendously unique. Powerful vampires could wander around in daylight, glow like the sun, move faster than thought, mutate themselves into any form, and so on. Individual vampires could opt into various myths: inability to cross running water, aversion to crosses, and so on– all via a point buy system. In The Requiem  (the current version of Vampire for their line), they are still not repelled by crucifixes, garlic or running water (by default), they have no need for home earth, and they can enter homes without invitation. But their powers are slightly more constrained– they’re lined up slightly differently, with a little less free combination of quirky powers.
Ultraviolet  took things in a radically different direction. For their mythology they selected a few vampire weaknesses from myths, decided that they were scientifically true, and extrapolated from there. Instead of stabbing vampires with a wooden stake, they discovered that the carbon of wood was the key factor… so the agents fire carbon bullets instead. Similarly, ultraviolet light is a spectrum found in sunlight that is less present in traditional indoor lights– and harmful to vampires. Guess what lights the agents armed themselves with?
So, I was thinking about the “vampires” in twilight. Honestly, if you had asked me what makes a vampire, what the core of a vampire was… I’d probably have answered that vampires must drink blood and are killed by sunlight. Just about everything else was negotiable– years of experience playing White Wolf showed me interesting ways of twisting just about everything else.
Then Twilight makes vampires sparkle in daylight. Really? That’s the big reason they hide? I ran with it, mostly because it was an easy read, and was enthusiastically recommended by my brother and several friends. It worked for me… but the word “vampire” was quite a hurdle. At least they kept drinking blood (even if they did make the heroes “vegetarians” in the White Wolf sense).
Lining twilight vampires up, we see some factors in common with traditional vampire myths (supernatural strength and agility, blood drinking, avoidance of daylight), several less traditional (no need for ancestral earth, no problem with running water) and her own unique takes (skin like stone, skin that sparkles like mica).
That’s pretty, but what about my world?
Just like all of the authors and game designers above, you can alter your monsters and make them truly your own. Is there a race you find awesome, but there’s some limitation put on them in the rulebook? It’s your world: shake it up by altering or eliminating those limitations. Maybe your Rakshasas are truly immortal spirits, quickly finding a tiger’s body to possess after their “death”– making them deadly long term opponents for your series. You could even borrow Zelazny’s  version and make them actual aliens. (Those Rakshasas could fit into many modern and sci-fi games…)
You could stop there: just alter the critter’s stats and be done. But the creatures we’re talking about are creatures of myth and legend– if you leave the myths as is, the players will wonder why everyone [including themselves] is wrong when they put a silver bullet in the werewolf and it shrugs it off.
Seeding Myths: A great way to handle this is to alter the myths that people tell about monsters. The spirit possessor Rakshasas probably deserve stories about one tormenting a village for generations after its first host was killed. You don’t have to go into great detail for each monster– but if the monster is important, or is going to recur, you should drop hints before the players run into it.
Lore and knowledge rolls can be a good way to pass information on when the PCs are gearing up– or even when they hear the roar of the beast. If wolvesbane doesn’t work in your world, let the characters roll to figure that out before they purchase the stuff. That said, there’s a very simple twist that gives the PCs a reason to be wrong.
Variants: Not everything creature has to match. If you keep some of your monsters stock, then when the PCs run into special versions, it’s perfectly fitting that their characters are surprised too. One GM used that perfectly on us in Ravenloft. At great cost our characters learned that lycanthropes were vulnerable to silver: Sython had a near death experience where he barely fended off a shape changing lady of the night when his sword was knocked aside and he grabbed up the silver dagger that he’d been gifted earlier that day. When we later learned (in combat, of course) that “greater werewolves” were immune to mere silver, the hierarchy of metals suggested our characters’ switch to gold. (I think it was a hint from a merchant in town about the “noble metals” that tipped us off.)
So now you have a few creatures altered from the norm. Maybe they’re based on the Grimm Fairytales instead of Norse Myth, or your Hydra is a great snake like the Greeks’ stories instead of the great dragon bodied beasts of D&D.
Decide how the creature interacts with the world. If there’s only one hydra in the world, and it has slain everything that encountered it, then you don’t need to worry about working tales of the hydra into your world. If, on the other hand, your campaign will feature vampires at every turn, you should begin planning on how you can reveal the differences. Scary tales around the campfire (told by an NPC, or even a PC with coaching) can alert players to the looming difference. If they’re a big feature in your game, you might even include the information (or at least teasers for the information) in the campaign pitch.
How have you altered creatures in your games? Did you change the myths of the game world to match? How did you work those revised myths and stories into your game? Please share your experiences in comments!