Most creatures of fantasy appear to be derived from these similar themes, but I wonder if I simply have not heard of creatures in other countries that hold captive the imaginations of the citizens in the same way zombies, werewolves and vampires appear to in the United States.
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The chupacabra, originally of Puerto Rico, now well-known in Mexico and thereabouts is a good example (they are well-established even in Arizona, where I live). Chupacabra has been profiled by the likes of Animal Planet. However, it has sinister, blood sucking attributes beyond what might seem like an otherwise harmless crypto-goat*.
*"Crypto-creature" is more accurate. Chupacabra prey on goats, but are not necessarily goat-like, though it is difficult to know with certainty. They do run on two legs, might fly and certainly can jump.
There are number of creatures that exist or are mentioned in Russian folk tales. They are pretty popular within ex-Soviet republics, mostly in Russia, Ukraine and Belorussia.
Some creatures I remember are:
Baba Yaga (a witch living in the forest, sometimes having "the bone leg", bakes and eats people who get lost in the woods - prefers little children. Hops around the forest in a levitational device called "stupa" which is a huge wooden mortar. Her accomodation is a wooden log cabin or hut elevated on a pair of chicken legs. The hut can move around the forest and follow simple voice commands. The hut is not very smart as in many folk tales it followed orders not only from Baba Yaga but also from random people, hunters, knights who happened to find it in the woods. Most of them get eaten by Baba Yaga anyway, so may be the hut is used to entrap them)
Koshei "the Deathless". An immortal skeleton, massively rich evil wizard\king of the forest, sometimes considered to be Baba Yaga's relative or boyfriend. His death is in the needle hidden in the egg hidden in the duck hidden in the hare hidden in (several more animals) hidden in a chest chained on top of some huge tree.
Vodyanoi (waterman) - lives in rivers\lakes, has commanding powers over Rusalki (mermaids, all females). Can drown people who in his opinion bring harm to rivers and lakes. Rusalki can drown people just for fun (males) or to increase own headcount (females).
Leshii (forest man) - similar to waterman, but lives in the forest. Each forest can have one or more forest men. Can either help someone who gets lost in the wood or lure them deeper until they starve or break the neck, etc. More random behavior and more dangerous than waterman.
Barabashka: common term for poltergeist- or ghost-like creature. Mostly harmless, but can be very annoying. Steals things, spills water, breaks mirrors. Lives in peoples homes, mostly rural. Not often found in big cities.
There are good articles on these subjects in wikipedia which make good bed time reading.
Trolls: Numerous tales about trolls are recorded, in which they are frequently described as being extremely old, very strong, but slow and dim-witted, and are at times described as man-eaters and as turning to stone upon contact with sunlight. Watch the movie Trolljegeren, it's a modern horror/comedy movies about trolls.
Huldra:The huldra is a stunningly beautiful, sometimes naked woman with long hair; though from behind she is hollow like an old tree trunk, and has an animal's tail. In Norway, she has a cow's tail, and in Sweden she may have that of a cow or a fox. Further in the north of Sweden, the tail can be entirely omitted in favor of her hollow or bark-covered back.
Mare: The mare is an evil spirit or goblin in Germanic folklore which rides on people's chests while they sleep, bringing on bad dreams (or "nightmares").
This question has kind of already been answered so I am just adding to the list.
In modern day Indonesia, the believers of polytheistic Hinduism wake up every morning and weave a basket from long grass in which they place a small cookie or biscuit, a flower, and a piece of incense. This ensemble then goes into something that looks like a small mailbox. Its purpose is to LITERALLY "keep the demons satisfied and happy" so they leave that house alone. You see these ALL OVER Bali. I would say that qualifies as a pretty strong belief in modern monsters, and it's population wide (Hindu only).
Many Native American and Native Canadian tribes still believe in various Nature Spirits / Totems. Though not really monsters, they do have plentiful stories about shaman who can shape-shift and the like.
Modern Aboriginals in Australia have a VERY strong belief in Ghosts.
Both China & Japan are OBSESSED with Anime monsters - e.g. your tentacle creatures, transformer type robots, etc. These guys get LOTS of print media - a Japanese comic shop is nearly wall-to-wall with graphic novels about these guys. Vampires show up a lot in Japanese stories as well.
In parts of the UK and Ireland, though the countries are by far predominantly Christian, there are still pockets of "true believers" in the Fey / Fair Folk / Faeries, though this belief is kind of watered down from the original stories to more like "garden sprites" at this point. There is a settlement up in the far North of Scotland where they grow crazy vegetables in impossible soil and they attribute it whole-heartedly and quite openly to the "Garden Devas."
Voodoo, though losing dominance, still actually holds sway a few places on earth as well, e.g. Haiti. That's more a belief in Black Magic and evil sorcerers however, rather than monsters.
Hope this helps.