Drool Hello

"Or else what, a monster's going to squirt goopy goo all over my face, huh, Ulrich?"
(splotch)

—Élisabeth "Sissi" Delmas, Code Lyoko, "End of Take"

What is the first hint that a giant monster, yet unseen, is towering over some characters, or clinging to the ceiling above them?

Not the vibration of its moves, the sound of its breathing, the putrid smell or anything like that...

No, in some case, the very first hint they'll get of this menacing presence is... some liquid splashing over their heads or shoulders.

Most often drool, though it can be other secretions. Sometimes this drool is acidic, and they're really in trouble. May be also the blood or remains of the monster's last victim for extra fun.

In a way, an organic form of Click. "Hello.", typically followed immediately by Oh Crap.

Also see Phlegmings. If the characters are inside a Cave Mouth, they may realize in horror that this is the cause of that drippy sensation.

Not to be confused with a first meeting combined with Perverted Drooling.

Examples of Drool Hello include:

Anime and Manga

Happens twice in Mahou Sensei Negima with the same occidental dragon in the underground beneath Mahora—first with Yue and Nodoka, then with Chisame getting drooled over the head—before they even notice the monster.
In Soul Eater, Eruka has a hallucination (one of several various characters have) of the Kisin doing this while she and Free are trying to revive him.
In one of the extra pages installments of the Skip Beat! manga, Maria has a rather large, remote-controlled, robot spider she uses to scare off women who get too close to Ren. Guess how she introduces it. Go on, guess.
Seirei no Moribito: Torogai runs into a cave in Nayug, seeking an escape route. Something splashes onto the floor beside her, and she realizes she's run into a trap. She gets out anyway... through the worm creature's digestive tract. Ick.
The disgusting Licking Woman from Junji Ito's Black Paradox series.

Comic Books

PS238 has a textbook example on this page, with Malphast accidentally summoning a tentacle... thing.
- Exploited by The Flea.

Films -- Animation

Hoodwinked semi-parodies this with when Granny is hiding up on the ceiling. A single drop of sweat falls right next to the Big Bad, and though he doesn't see it he realizes she's there because the drop smells of hairspray.
One The Land Before Time movie involves this. Although Cera's companions see the Sharptooth coming, she doesn't notice it (thinking it's a gag) until it starts to drool on her.

Cera: (screams) Sharptooth drool!

In Alpha and Omega, the bear slobber on Humphrey after he accidentally hurts the bear's child.

Films -- Live-Action

Happens indirectly in Men in Black. After K enters the morgue to find out what's happened to J, he tries to light a cigarette but the match is put out by a drip of slime. He looks up and sees the attendant glued to the ceiling by the Bug's secretions—a warning that the Bug is present in the morgue.
The Harry Potter and the Philosopher's Stone movie: the gang is alerted to Fluffy's presence by his drool on Ron's shoulder. Notably, they're aware he's there; the drool just lets them know he's awake.
This happens in the remake of The Blob, just before the Blob kills the quarterback. There, it is slime from the Blob itself, making it much worse.
Journey to the Center of the Earth. In the 2008 version, Sean Anderson hears a noise and hides behind a giant boulder to escape the threat. Said prehistoric threat drools on him while leering down above the boulder.
I Still Know What You Did Last Summer. Frightened teenager peers into her closet. Seems like a red herring, until blood drips under her feet and out pops a bloody hung corpse.
Jurassic Park: The severed arm scene.
Deep Rising. As the remaining group of survivors discuss what to do next, one of the monsters drips slime/drool onto the comic relief's shoulder. The comic relief proceeds to spaz out and opens fire on the monster, causing it to split and spill out the partially digested (but still alive) remains of another character.
The Alien franchise is pretty fond of this one. Whenever dripping saliva onto the victim won't signal a Xenomorph's presence, the warm air exhaled onto the victim's neck from behind will. And if that happens, it's already too late to run.
In King Kong (2005), during the sauropods' stampede, Bruce Baxter takes cover against the wall of a ruin... only to be drooled upon by one of the smaller carnosaurs above, about to attack him, forcing the actor to flee again.
In the first Hellboy movie, this is how the title character (and the audience) is introduced to the demon Sammael.
In Bad Moon, it happens to the forest ranger before he is killed.

Live-Action TV

Subversion: In Star Trek: Deep Space Nine, there is one episode in which the liquid dribbling from the ceiling is a dead shapeshifter (their true form is liquid).
Angel episode "Parting Gifts". Wes informs Angel that the demon he's chasing can be tracked via the Alien Blood it's leaving behind... like the kind that's now dripping on his shoulder.
The Day of the Triffids (2009). After Torrence launches his takeover bid, Mason and Cocker are taken out to the woods to be fed to triffids. An armed mook is ordering them out of the back of the truck when triffid venom drops on his shoulder, then one of the Man-Eating Plants yanks him screaming into the air.
Sort of in The X-Files. In "Squeeze", Scully is alerted to the fact that Tooms in in the air vent when a bit of bile drips out of the ceiling.
In an episode of Sanctuary, a nosy journalist notices a corpse dangling above her when some blood drips on her face.

Video Games

Happens in a StarCraft cutscene: Fenix is walking along a hallway when slime drips onto him. He looks up... to see two hydralisks coming after him.
Resident Evil 2. Shortly after entering the police-station, you're introduced to your first Licker this way. They do so enjoy crawling on the ceiling...
Early on in Metal Gear Solid 4: Guns of the Patriots, Snake is alerted to the presence of a Gekko by the drips of blood coming from its latest victim.

Visual Novels

In Snatcher, blood drips from the ceiling in Cunningham's office. Upon glancing up, you see his Snatcher grimacing back at you.

Web Comics

Happens to Vaarsuvius from The Order of the Stick in the strip aptly titled "Good to the Last Drip". It is seawater here, but the effect is the same.
There's a variant in Zebra Girl where the victim is smoking, and the monster coughs.
In Intragalactic, the Roboticist is alerted to Ben's presence by a drip of ice cream. The author also outlines the trope in the commentary section.
A particularly squicky variation happens to Jenna in Bloody Urban: she gets slime dripping off of a Blob Monster in her tea. (Not that she's really in any danger—he was only on the ceiling so he could charge his iPod.)

Western Animation

Happens to Sissi in the Code Lyoko episode "End of Take", with a helping of Tempting Fate a few seconds before, providing the page quote.
In The Spectacular Spider-Man, a bystander attempts to hide from the Lizard's rampage through a subway station by ducking into an alcove. Cue the drips of saliva falling on her head. She manages to survive via Spider-Man's timely intervention.
Michaelangelo is the drool-ee in the Teenage Mutant Ninja Turtles 2003 bonus episode "Mayhem From Mutant Island". The drool-er is a mutant dinosaur right behind him.