Welcome to the NHK: Satou's upperclassman drops her cellphone into the sea as they travel towards mass suicide on an island.
In Real Bout High School, Kyoichi Kunugi crushes his cell phone in his hand after being informed by his employers that if he doesn't cooperate with them his family will be killed. Of course, that was an act of rage rather than an attempt to free himself, and he did go ahead with his boss' plans, if grudgingly.
In Code Geass, during Lelouch's Heroic BSOD in response to Nunnally being viceroy of Area 11, he snaps his cell phone in half and throws it out the window of a moving monorail.
A Corona beer commercial had a person relaxing on the beach skipping rocks. The pager on the table starts making noise, and so they casually skip the pager into the ocean. Another Corona commercial has a pan across a beach to a man sitting back on a chair with a Corona Light and settles on his cell phone while the slogan "Miles away from ordinary" note may not be the actual slogan.) is dubbed over the screen. His cell phone? It has no service, letting us believe he walked all the way down the beach to a place with no service instead of, y'know, finding a quiet spot and just turning it off.
There was a Corona ad here in Mexico a few years ago that had a similar theme, but it was a lot more subtle. It was a shot of a guy in a poolchair (only the arm is visible), and next to him, on a little table, there's a cellphone and an ice-cold Corona. The phone is ringing and the guy just ignores it, taking the beer bottle instead. Placid beach waves and the phone ringing are the only soundtrack.
There is yet another one where the phone gets casually dropped in the water.
Subverted, obviously, in a Motorola ad. A forty-something man starts getting rid of all his material wealth: he tears off his necklace, drops his watch, and throws his diamond ring in the street. But when it comes to his Motorola phone... of course, he keeps it!
At the end of Hook, Robin Williams rediscovers the phone his wife had thrown out the window earlier in the movie. He then tosses it back out the window himself.
Occurs humorously in Wild Hogs. The three main characters are going on a mid-life crisis road trip, one brags about how his phone has a GPS so they won't get lost, and his friend takes it away and throws it in a fountain. In retaliation, the first takes his phone away and tosses it. Not to be outdone by the other's expressions of freedom, the third (perpetually unlucky) friend tosses his - right onto the windshield of a semi truck. A semi truck with a very large and unhappy driver.
Cypher throws his cell into the trash in The Matrix. This, combined with his talk to Smith early on, is basically a signal that he's no longer working for the Resistance and has sold out to the Machines. That, and he leaves it on when he chucks it; the Agents use this to trace their location.
Mind you, throwing away your cell phone pretty much SOP for Neo and Co, if the line is being traced and they need a clean cell. In Cypher's case, he called the Agents and left the phone outside the building that Neo and co. were going to use as their exit, allowing the Agents to set their trap.
In the Russian movie Irony of Fate: Continuation, Irakliy (a manager in a cell phone company) is nagged by phone calls throughout the entire film. In the end, he gives it to a random kid as a New Year gift.
A pre-cellphone era example occurs in The Man In The Santa Claus Suit, when an overworked political speechwriter finally destroys his pager.
In For Your Eyes Only, James Bond leaves his communicator watch on a perch with a parrot, who then drops it into the ocean. Not that Bond was quitting; it's just that having a Two-Person Pool Party was a damn sight more interesting than talking to the Prime Minister.
In Identity Theft: The Michelle Brown Story, identity thief Connie Volkos flushes her cell phone down a toilet when the detective handling her victim's case calls and offers to help her if she turns herself in. (Since she's committing ID theft mostly to lead a better life than the desperate one she's led so far.)
In Final Fantasy VII: Advent Children, Tifa points out that although Cloud doesn't answer his phone, he never Cuts the Electronic Leash either. Later on, though, he loses the phone in a fight.
In Broken Arrow (1996) Deakin (played by john Travolta) used an electric shaver to simulate static noice in order to break off the communication via radio.
The father of the main character in Prehysteria 2 violently throws his ringing phone against the wall, breaking it.
In Tucker & Dale Vs. Evil, one girl among the college students, thinking they're in a slasher movie situation, pulls out her cellphone to call the police. Which Chad (the leader) grabs and throws into the lake, not allowing anyone to be Genre Savvy. He delusionally sees himself as the hero in a slasher film, and he refuses to let anyone break a cliche.
In Alias, Sydney Bristow, at the edge of breakdown, reacts to a call from her boss at SD-6 by tossing her cell phone. Vaughn notes, "You just threw your cell phone into the Pacific." They both have a good chuckle.
Eerily echoed in Season 5, when Sydney is caught in a Lotus-Eater Machine and she throws the same phone away, twice in a row.
Also happened in the UK version of Queer as Folk: Vince had a date and kept nattering on the phone to various people who were bugging him and Cameron grabbed the phone and tossed it into the canal. This is a slightly different angle because it wasn't Vince's work that the phone represented so much as his willingness to let other people use him (so Cameron grabbing the phone was his way of saying "be selfish for once in your life").
In the Star Trek series this doubles as an Insignia Rip-Off Ritual: a crewmember decides to do what must be done and puts aside his or her communicator (it's even more of an electronic leash than a cellphone, since the communicators are also tracking devices.)
Done on UK sketch show Smack The Pony: A character throws her phone into a lake. She immediately regrets it and goes into the water to look for it.
In Dollhouse, Victor's imprint throws away DeWitt's phone for her, as she tells him how often she's complained about how slippery it is.
Used at the end of one of the episodes of the (short-lived) revival of Fantasy Island from 1997. The man who has realized that neither getting ahead in business nor reliving his own childhood is not as important as spending time with his son throws his cellphone into the ocean. Of course, this being Fantasy Island, Mr. Rourke retrieves it from his fish tank (providing a sensible alternative to the usual version of this trope.)
On I Love Lucy, Lucy keeps getting interrupted by the phone when she's trying to tell Ricky she's pregnant (excuse me, "'spectin'"), so she finally throws away the receiver, saying, "Darn that thing!"
In Scrubs, when JD thought that Dr. Cox didn't care about him any more, he threw away his pager. By the end of the show, Dr. Cox finds it and returns it to him lobs it and makes him fetch it, berating him all the while. JD is elated at this turn of events.
In the UK version of The Office (UK), Tim takes off his microphone (to pick up his speech, as per the Mockumentary setting) in order to presumably admit his feelings to Dawn.
Has happened a few times on Home and Away. Romeo threw his into the Pacific, while Roo put her SIM card in a cup of coffee.
Averted in NCIS; Gibbs often damages his cell phone, but this is portrayed as a character flaw, a part of his somewhat curmudgeonly ways. On one occasion, he breaks his phone, hands it to one of his subordinates to fix, and they replace it with one of the several identical phones they keep in a drawer. By contrast, McGee is depicted as sometimes being overreliant on technological solutions.
Usually Played for Laughs, though. During one episode where the team is exposed to a bioweapon, all of their gear is confiscated and disposed of. Gibbs starts giving orders to McGee, who complains about not having his PDA. When told to "use Ducky's", McGee fruitlessly searches for over a minute, before Gibbs exasperatedly yells, "McGee! It's a pad and a pencil!"
Ultraviolet. The expensive cell-phone of one character is seen thrown into a trash bin, as a sign that he's become a vampire (the voice of a vampire can't travel over a phone line).
Deconstructed in The Office (US); Michael and Dwight take Jim's phone off him on a road trip and gleefully throw it out the window. Cue Jim telling them that the only photos of his brother's new baby were on there, and they sheepishly stop the car and walk down the side of the road looking for it.
A pre-cell phone version of this trope occurs in Family Matters, when Lt. Murtaugh gives Carl a pager and keeps using it to beep him over the most frivolous of things (such as needing help with a boil). Eventually, when he does it while watching Laura perform Romeo and Juliet, Carl takes the pager and stamps on it.
A song by Cake is completely devoted to this.
"No phone, no phone. I just want to be alone today..."
Metal Gear Solid 3: Snake Eater does this in the ending, where EVA throws Snake's ringing radio (on which he's been getting calls about his mission entire game) into the fire, and Snake, rather than protesting like he normally would, proceeds to....well, the two have a very interesting night together.
Cloe does it at the end of The Secret Dancer, though with a walkie-talkie. Bonus points for having the battery case fly off as it hits the floor.
Charlotte does this at the end of The Rugrats Movie, but she doesn't abandon her job. It's just that her reunification with her lost daughter takes precedence.
Happens in Rocket Power when Sam's busy, divorced dad back in Kansas spends some time with him. Though here, he just tosses his phone in the backseat of the car as the two drive off to spend that lost time together, and they laugh as the phone rings.
Several religious and secular movements and even some health specialists (including those not specializing in mental health) have advocated periods of isolation from communication networks, with reasons including realignment with some higher power, stress relief or reducing dependency (psychological or otherwise). Of course, the concession is often made that such sessions should be scheduled to avoid clashing with the rest of one's affairs and those that might need to make contact should be informed that one will be unreachable.
The Amish are practically the Ur Example of this- according to one source, they adopted telephones just as much as many other Americans, but for various reasons (linking to the outside world, promoting idle gossip, generally weakening community values/institutions etc.), having a phone in Amish homes was banned in the 1910s. This being the Amish, they've replicated this with pretty much every other technology tying them to the outside world.
Ironically, with the advent of cellphones, some Amish communities have reintroduced phone usage (that bit about phones? It forbids "wires to the outside world"). They use car battery rigs to recharge them.