Television Portal

You're watching television when suddenly the screen turns to static. A face appears, dark and scary, but you're not worried. After all, it's only the television, nothing can happen. But then it moves closer and closer, so close that it starts reaching out from the TV screen. Now you're very, very scared.

Welcome to the Television Portal. Most often a form of Nightmare Fuel ('cause who wouldn't be freaked out by a television image coming to life?) and Paranoia Fuel (do you know how many hours of television you watch?). Sometimes results in Up the Real Rabbit Hole, Trapped in TV Land, Refugee From TV Land. May start when The Television Talks Back. A quite literal version of The Fourth Wall Will Not Protect You.

May extend to coming out or going into a television set or other electronic device with a screen (i.e. a computer).

Compare Reaching Between the Lines (the same effect, but used as comedy). Often a case of The Fourth Wall Will Not Protect You.

Examples of Television Portal include:

Anime and Manga

Urd from Ah! My Goddess does this on a regular basis - It's one of her modes of transit.
The Digidestined/Chosen Children (predominantly in Digimon Adventure 02) use computers to travel to and from the Digital World.

Comic Books

In the Bongo Comics crossover "When Bongos Collide!", Kang's and Kodos's ray zaps the Simpsons's TV, causing Itchy and Scratchy to emerge from the set and, through their constant fighting, wreak havoc in Springfield, culminating in a core meltdown of the nuclear plant.
Dark Entries, a graphic novel about John Constantine, features a storyline which takes place in a gameshow in Hell. One character, Jude, sticks his face in a television screen to see what's on the other side; it turns out it's a portal out of the aforementioned Hell.

Film

Samara/Sadako in The Ring.
Parodied in Scary Movie 3 with a Samara look alike.
Videodrome Here, though, the protagonist actually sticks his face into the television.
Poltergeist. While Carol-Anne is watching static on a TV, a ghostly hand comes out of the TV, waves around and eventually dives into the wall.
In A Nightmare on Elm Street 3: Dream Warriors, Freddy Krueger kills one girl by popping out of the television, although his head comes out of the top and his arms come out of the side, rather than out of the screen. His victim ends up with her head smashed into the screen.
- Spencer is pulled into a video game by psychedlic tendrils that emerge from an old television in Freddy's Dead: The Final Nightmare.

Literature

Happens twice in John Dies at the End.
Inexplicably done by Jason in Friday the 13th: Hell Lake.
Done a few times in the Dream World in A Nightmare on Elm Street: Protege.

Live-Action Television

In the Doctor Who episode "The Time of Angels": "Any image of an Angel is itself an Angel." Thanks a lot, Moffatt.
Are You Afraid of the Dark?: In the episode "Tale of the Crimson Clown" the titular clown doll is shown reaching out of a television when trying to attack a bad kid.
Happens in the first episode of The Outer Limits, "The Galaxy Being."
Sort of used in the Fringe episode "No-Brainer," where a video on the web that melted people's brains caused them to first hallucinate a hand that reached out from their computer screen.
ITV's modern day adaptation of A Christmas Carol had ~~Ebenezer~~ Eddie's father climb out of the tv to talk to him.

Music

David Bowie's "TVC15" has the protagonist's girlfriend crawl into a TV set and never come back: by the end of the song he's wondering whether to follow her or not. Yes, this is from his "cocaine madness" era.

Video Games

Persona 4. When you first encounter the Midnight Channel, the screen on the protagonist's television first goes to static before showing the image of a girl. The protagonist then touches the TV and HOLY CRAP MY HAND'S GOING THROUGH.
Toyed with in Dreamfall: Faith definitely gives off a Samara/Sadako vibe when she appears on TV screens after it is briefly obscured by static. However, she never actually comes out of said screen, only talks through it. Also, in The Longest Journey, there is an optional scene where Fiona's TV screen acts as a portal to Arcadia, bringing magical creatures from it into the room. However, they quickly disappear, and everybody thinks they saw a weird dream.

Western Animation

Happens on The Simpsons (of course) when Itchy and Scratchy smash the Simpsons's TV screen with axes and climb through the hole in a "Treehouse of Horror" special.
The Fairly OddParents episode "Channel Chasers" turns television into a world of flying television each leading to a new channel.