Harassing Phone Call

There's nothing more unnerving than receiving a unknown phone call in the middle of the night. Except, of course, receiving an phone call that consists of silence for a moment before you start to detect sounds of heavy breathing or fiendish laughter on the other end before the caller hangs up; the caller may even be an obsessive stalker that will keep calling you, even after you tell them to stop it. Sometimes there may just be a phone ringing and no one answers on the other line or someone just called and hung up without even talking.

Sometimes the voice initially sounds so charming and trustworthy that you can't help but strike up a conversation with the person. When this happens, the caller then switches their kind tone for a more menacing tone and you suddenly find yourself wishing that you had not answered the phone at all. Particularly when you find out that The Calls Are Coming From Inside the House.

Examples of Harassing Phone Call include:

Anime

In Perfect Blue after Mima quits her job as a pop idol to begin a career as an actress she starts receiving threatening messages and phone calls from her stalker, Me-mania.
One of the more disturbing scenes in Higurashi no Naku Koro ni involves Keiichi taking a phone call from a distressed Shion, who supposedly went missing a number of days previously. He has only recently found this out, and pleads with her to tell him that he's wrong. All she can do is sob. He then begins to poke holes in her confession that she spoke to another person who went missing around the same time; if she's telling the truth, the only way she could have spoken to them is to have done so after they went missing. There's a moment of silence after he points this out to her, and then she begins to laugh hysterically. Without another word, she hangs up.
- The PS 2 version of the scene is much creepier. The scene plays out the same right up until the moment of silence. Then Shion starts laughing in a more psychotic style than the anime, then out of nowhere, the volume suddenly become ten times louder as the screen goes, black, is then filled up with text that is Shion's laughter, and then we get a shot of Shion in a completely dark room where all that can be seen is her face, which can be only describe as a clown-esque deranged smile, all while the laughter goes on.
In episode 11 of the anime Ghost Stories Satsuki keeps getting these from a Creepy Doll named Mary.
One episode of Paranoia Agent has a woman with multiple personalities get numerous harassing phone messages... left by her other personality.
Death Note: Near keeps calling and harassing Light at odd hours of the day and night and hanging up.
In Koharu no Hibi Koharu, Akira's stalker and Yandere, quite frequently calls and texts him.

Live Action TV

Law and Order and other Crime Drama often use the fact that the Red Herring is getting them (after it's become clear that they're innocent) to show that their life has been ruined (I recall a specific example in SVU where a care worker is Driven to Suicide by them after the detectives discover she's failed to make checks, leading to the death of a child and the torture of another).
The one off BBC drama series Pig Heart Boy (about a boy who receives a heart transplant from a GM pig) has the fact his parents have been getting these as the reason his parents had been acting so stressed.
Ryan's obsession with Dr. Nathan in Oz led him to write letters and call her non-stop. It unnerves her to the point where she eventually tells him to cut it out. Unfortunately, this makes his obsessive behavior even more extreme.
Played for Laughs in one episode of the Britcom Nelson's Column, in which The Ditz is phoned by the police and told a phone perv is going to call her and they need to trace the call, so could she keep him talking. So she discusses her underwear with him for ten minutes, before Nelson asks her what's going on and, on being told, asks "How would the police know that?"
Are You Afraid of the Dark?: In the episode "The Tale of Laughing in the Dark" the character Josh is talking to his friend on the phone when the Monster Clown Big Bad of the episode suddenly speaks up on the other line "If you don't give it back, I'll come up and get it!"

Film

The killer in Scream does this several times, most notably in the opening "Casey's Nightmare" sequence.
- This is parodied, of course, in the Scary Movie movies.
A Nightmare on Elm Street, before it got all schlocky. Nancy tries to call Johnny Depp to warn him not to go to sleep. Then the phone rings. She picks it up. It's the sound of Fred's claws being sharpened. She (understandably) freaks out, tears the phone out of the plug, and throws it across the room. Then, despite being unplugged, it starts ringing again. This time, it's Freddy again, telling her that "I'm your boyfriend now, Nancy, and then he sticks his tongue down her throat, through the phone.
Played for comedy in Serial Mom. "Pussy Willows!".
Alex calls Dan repeatedly in Fatal Attraction, but when he keeps ignoring her, she gets more and more unhinged.
Spider Man: Peter is worried about Mary-Jane and calls her home to make sure she's okay but instead of Mary-Jane he gets the Green Goblin on the other line who giggles and says in a creepy sing-song voice, "Can Spiderman come out to play?"
Lost Highway: At Andy's party Fred meets a strange looking Mystery Man in Black who tells Fred that he is at his house right now and is the one who sent the videotapes to him. He then tells Fred to phone his house, Fred does so, and the voice of the Mystery Man answers at the house while he's standing right in front of Fred.
The Ring: Whenever someone watches the cursed video tape they receive a phone call with a child's voice on the other line warning, "Seven Days."
Black Christmas featured disturbing phone calls throughout, as did the 2006 remake (though far fewer, and considerably less disturbing).
The Peacemaker. George Clooney's character knows that the Renegade Russian he's after is in a truck stuck in a traffic jam near a war zone; he can see them via satellite but can't tell which truck it is. So he call his old enemy's mobile and makes him think a cruise missile is coming down on his head. The Russian naturally loses his cool and pulls the truck out of the traffic, giving away his position.
In The Crush Darian does this to Nick.
Ramsley calls Jim in The Haunted Mansion before hanging up without answering.

Literature

In the novel The Wind-Up Bird Chronicle by Haruki Murakami, the main character, a married man, keeps getting calls from some random woman trying to initiate phone sex. It's his wife. Maybe?
Referenced in the Temps story "Sortilege And Serendipity" by Brian Stableford, where one of the Talented kids has the superpower to pick up a telephone and tell you where everyone who used it in the last day is now. He's nicknamed "the Phone Freak Kid", because tracing these people is the only use anyone can see for his powers.
In Dirk Gently's Holistic Detective Agency, Susan Way gets a number of phone calls with nothing but the sound of faint wind whistling. She's more perplexed and annoyed than frightened, describing it as a minimalist heavy breather. It's actually the ghost of her recently-deceased brother Gordon, trying to complete the phone call he was making when he died.
In Peter Moore's "Caught In The Act" Ethan receives frightening ones from Lydia.

Music

German band Die Ärzte made a song about this, "2000 Mädchen" (2000 girls), which is told from the POV of the caller.
Rockwell's 1984 hit "Obscene Phone Caller".
"It's Me Again, Margaret" by Ray Stevens is a darkly comic version.
The Weird Al sung-by-a-stalker song "Do I Creep You Out?" (sung to the tune of "Do I Make You Proud?") has the lyric:

Call you every night and hang up/ Gonna carve your name in my leg/ In my leg, oh, oh!

Video Games

In Silent Hill 3, Heather gets a number of harassing phone calls dropping unsubtle hints about her true nature.

Western Animation

Family Guy: Peter gets these from his boss Angela in the episode "Peter-assment". Also, while the Griffin's were out on vacation Herbert kept calling the house and leaving creepy messages for Chris.
SpongeBob SquarePants: In one episode Spongebob gets a phone call which consists of a jelly fish breathing heavily on the other line before hanging up.
In the Invader Zim episode "Bestest Friends" Zim gets a best friend named Keef in order to be seen as more 'normal' by the other students. However, when he tries to get rid of him Keef becomes something of a stalker towards Zim. One scene features Keef calling Zim right after Zim tells him to go away and Zim reacts by pulling the phone cable out of the wall.
Hey Arnold!: One of the ways Helga keeps reminding Arnold he has "24 Hours To Live" is by repeatedly calling him.
A Freaky Stories story involves a babysitter constantly being called and asked "Have you checked the children?". She loses it when she finds out the calls are coming from a second line in the house, but it's strongly implied that it was the children making the calls.
One Halloween Special episode of The Simpsons hilariously subverted this trope when the family accidental ran over and killed Ned Flanders. Homer later receives a creepy stalkerish phone call from a raspy-voiced psycho, but when he replies to the caller it turns out that the caller is his friend Moe the bartender, who accidentally dialled a wrong number while trying to stalk Ned's wife Maude.
American Dad: Francine tries to prove to Roger that Stan cares about him by using a voice modulator and pretending to hold Roger for ransom. When she returns home, Stan is nonchalant and gives surprisingly elaborate explanations for Roger's absence. Ultimately he tells Francine that Roger's people came back for him, and if they stood on the roof waving kitchen utensils they'd receive a special telepathic message. While they're waiting, Stan points out that they have caller I.D. and Francine was using her own phone.

Web Comics

Silent Hill: Promise: Vanessa is continually harassed by a "Weird phone lady" (later revealed to be named Marissa) who wants her to leave town. Admittedly, given the very nature of Silent Hill, Marissa could be trying to save Vanessa's life, depending on how the story unfolds.

Web Original

The Annoying Orange: In a parody of "The Ring" a guy gets a call from Orange after watching a cursed video tape who laughs repeatedly and warns him that in seven days he and his friends will become onion rings.

Real Life

Harrassing phone calls are the bread and butter of bill collectors. The FDCPA limits calls to between 8 AM and 8 PM, though not every collector honors this.
Less Truth in Television than it used to be, thanks to telemarketers. More people use answering machines and caller ID to filter phone calls, rather than picking up every call. It used to be that any incoming phone call was viewed as important; now they're viewed with suspicion.
Let's not forget obscene phone calls, where the caller gets off on delivering sexual or foul language to an unknown called party, and which to the person receiving them is a form of stalking and sexual harassment. Making such calls in many cases is a class 1 misdemeanor. Even without Caller ID, the phone company logs such calls, so the perpetrator's phone number can be discovered, but most people who regularly engage in this nowadays use prepaid cellphones or payphones, which requires a more extensive investigation.
Senior Power, an old movie meant to teach old people to defend themselves from crime (and mockingly reviewed here), includes the "obscene phone call" scene. Apparently, when someone harasses you over the phone, the right thing to do is to... whistle really loud into the phone. So that the harassing caller will freak out and fall over.
- It works. Thing is, you don't just put your lips together and blow, you use a pea whistle such as sports coaches use, and you can seriously inconvenience (if not deafen temporarily) the harasser. I've tried it, (although I am not elderly) and the ex-boyfriend I suspected was suspiciously hard-of-hearing at work the next day! Or so I heard...)
  - When the sports whistle failed to deter the little freaks calling my teenage cousin, my uncle went to the next level; a handheld air-horn. He used it once—and they never got another call after. (Nowadays, he'd probably get sued, but this was in the early eighties, and he never heard a word about it.)
An unfortunate television ad campaign in France for phone company 9 Telecom featured a man being accidentally harassed because his name sounded like the company's... Which triggered a slew of harassing prank calls in real life.
Genevieve Sabourin, alleged stalker of Alec Baldwin supposedly called and texted him a lot.