Zombie movies, first among them being, of course “Night of the Living Dead” has the whole world aware of the problem. With newscasters giving out helpful information and updates.
I am Legend does count.
You just have to know who the monster is.
As far as the Buffy-verse in concerned, I’ce always seen it like this:
Up till the end of season 3, very few people knew about monsters and that sort of thing. However, after half the town saw the mayor transform into a 100 foot snake demonn…well…they started to understand all the weird stuff that happens in Sunnydale. After that, it was a combo of the know, but don’t say anything, and denial. Sort of, if I ignore it and pretend it doesn’t happen, it will go away/not hurt me. I mean, come on, there’s only so many dead bodies with two puncture wounds in the neck you can find before you finally start to agree that yes, it has to be vampires.
In Angel it seems different, though. I’ve only seen a few eps, but some of those are the last few of season 4, where pretty much the entire wolrd was under some spell-like thing, and then was not and saw Jasmine for the horrible monster she was (not to mention the sun being blotted out for a long time earlier to that.) So maybe the rest fo the world pulled a Sunnydale and went into denial mode, or there was some weird thing about it that affected their memory, so they forgot about it.
The Vampire Hunter D anime is set in a future where vampires zombies and othe monsters are all too well known.
In Robin McKinley’s Sunshine, the general public is aware of vampires and human-demon crossbloods. There’s a special police force that deals with them, though it turns out
that most of the agents in the special police force are human-demon crossbloods to begin with
The main character, Sunshine, is the daughter of one of the better known magical families, though most of her paternal relatives disappeared in what is referred to as “The Voodoo War”. I did like the phrase most people used to refer to the bodies left behind by vampires - “dry guys”.
I’m very surprised that I’m the first person to mention Godzilla. In the first movie, of course, the big green guy is new and startling, but, in just about every giant monster movie following that, the entire Japanese population seems to know all of the giant monsters (perhaps through spotter cards), and helpfully yells out their names as they appear.
Does Sesame Street count?
At least as high a 5, yes. 
At least as high as 5, yes.
I’m not 100% sure, but it seemed that in Van Helsing the general public knew what he was charged to do. And the town in the main part of the story was obviously aware of the Dracula menace.
Sounds like it was perhaps at least loosely based on a few of the Vampire stories mentioned above.
There are lots of zombies in the Old Kingdom series. Everyone knows about them.
In Sunshine, there are suckers (vampires), demons, were-whatevers, and succubi/incubi. They’re collectively known as Others, and the book is set just after an Other/Human war. At the coffeeshop there’s one known demon partblood and a were.
“Cut off the Head or destory the brain”
Zombies tend to be the big one, because in most media, zombies aren’t particulary subtle and aren’t smart enough to try to hide or blend in.
Gonna throw in some Sci-fi into all this Fantasy stuff.
Certain of Heinlein’s worlds come to mind. Espesially the guys in Glory Road. They were impressed with how Oscar handled Igli.
Monsters Inc. (All the monsters know they are real).
Aliens People know the monsters exist.
*Monsters Inc. *
The monsters know, but the humans don’t.
*Aliens. *
At the beginning, nobody seemed to believe Ripely, except for burke, who thought it sounded interesting enough to send someone to look for it. The marines sounded pretty skeptical as well.
Dropship Pilot"Aparently, she saw an alien once"
Hudson:“Whoop de fucking do!”
It wasn’t until they got ambushed that they seemed to take the whole thing seriously.
In fact, in all of the Aliens movies, there’s the implication that nobody knows about these things except ripley and the big orgnization who is trying to exploit it, or at least somebody withen it. The general public, as much as we see them, doesn’t seem to have a clue.
Yeah, but one of the marines (the butch female one) makes a comment like “So, this is another bug hunt.” This implied, to me at least, that the marines had hunted the aliens before.
My guess, re: Aliens, is that other extraterrestrial life had been discovered before, but not specifically the “Xenomorph” aliens encountered by Ripley. And probably nowhere near as dangerous as the Xenomorphs—I’d guess something more along the lines of Earth vermin, or smallish predators, that were disturbing colonial operations.
Another possible interpretation is that the marines have been sent out to capture an alien before but every time it was a false trail. A “bug hunt” in that case would mean “another mission to catch something that doesn’t exist.” This attitude would fit in with the other remarks made.
Possible, though there’s one theory that Aliens was a Vietnam allegory(superior force fighting off an enemy that seemingly comes out of nowhere). I’ve heard somewhere that “Bug Hunt” is used by the modern military when looking for elusive targets(Like, say, OBL).
I always wondred what the marines were used to fighting before this. You don’t need a dropship full of missles, smartguns and that big APC to kill animals…