An episode of Psych has Shawn's father discovering Crackdown. Cue them returning the next day or so, and the father hasn't slept and has to be prompted to stop, and even threatens Shawn when he tries to take the console away.
Shawn's Dad: ...it lets you feel like a cop, without all the guilt after you shoot someone.
In one episode of The Big Bang Theory, Penny gets addicted to Age of Conan. At one point Leonard asks why she's not at work, and she says she doesn't work on Mondays. He then points out that it's Thursday. She finally says "Okay, I need to stop" when she gets hit on by Howard in-game and actually responds positively.
In the penultimate episode of Angel, Spike leaves Illyria guarding Drogyn and offers them Crash Bandicoot 1996 to pass the time. This leads to:
Illyria: "I play this game. It's pointless, and annoys me. Yet I am compelled to play on."
In an episode of Star Trek TNG, a woman shows Riker a small video game which gives the user a direct endorphin rush when they complete a level. Riker plays it, quickly becomes addicted, and spreads it to rest of the TNG crew.
In the comic strip FoxTrot, Jason's video game obsession transfers to his mother who plays for days and days before realizing she has a problem/is getting cut off.
One series of strips had Andy getting addicted to Nintendogs; when she finally returns Jason's DS, he (rightly) guesses that it's only because the battery died.
Video Games (must be referenced by the game in some way)
The Civilization series lampshades this trope. The advertisement surrounding Civ 4 use the phrase "one more turn" as a Madness Mantra, including starting a fake site for Civilization-holics called "No More Turns". When you reach the "end of history" (win or lose), the options given to you are "End game" and "Just...one...more...turn!"
Civ 4 also included, in the options menu, an alarm, that you could set to go off at a set time or after a certain number of minutes hours had elapsed. How effective it is is doubtful, but bless them for trying.
Also shows up in Elemental - War of Magic which despite some growing pains shortly after launch still proved itself to be ridiculously addictive.
Lampshaded In Stronghold, If you play for hours (or days, or weeks, or months...) The Scribe says things such as "How about a snack, sire?" "You haven't slept for days sire!" "It's getting late, sire, Aren't you tired?"
Dungeon Keeper displays messages to the user reminding them to take a break. Unlike some of the other examples listed, these are based on the system's internal clock instead of play duration.
...do you want me to give human kids an addictive video game that will deprive them of their sleep?
Disgaea 3 gives a trophy for leaving the game on long enough.
Tales of Vesperia has a similar Achievement which you earn by having a save file over 100+ hours long.
Part of the backstory of strategy game This Means War! is a somewhat post-apocalyptic setting caused by a dangerously addictive videogame that players were so hooked on that they neglected their duties (for instance, maintaining nuclear power plants) to keep playing.
The developer of Desktop Tower Defense has admitted to tweaking the game to encourage more play. He regularly gets emails from people asking to "please ban me from the game, I can't stop playing".
In EarthBound, if you play long enough without saving, the main character's dad will call you to remind you to take a break.
Sins of a Solar Empire is advertised on the box as something like "all the 'just one more turn' addictiveness of a TBS like Civ, but with no turns so you never know when to stop!"
Referenced in LittleBigPlanet 2, where playing after 9 PM earns you the "Just... One... More... Go..." trophy.
The Sims addressed this in the first game's strategy guide, when referring to "Winning the Game". Don't be absurd. This is a Maxis game! What's to win? You and your sims can play unto perpetuity, getting into entanglements and trying to get out, and by the time you know it, it will be 3am your time, and you don't even have your teeth brushed...
Snood has a "Just One More Game" option that automatically closes the program on your computer after your next attempt, but not before a pop up window says, "You said one more game. Snood will now quit. But no one will know if you start again". Evil!!
There is a shirt on the Minecraft Store that says "Just One More Block" four times in a row!
Lampshaded in Dungeons of Dredmor, where it asks if you try to quit: "Just one more game wouldn't hurt, would it?"
Lampshaded and inverted on the menu screen of Aoi Shiro, where, depending on the time and day of the week your computer is set to, the character will tell you to go do your homework first, your house chores, go to school, or even to go to sleep.
Using the appropriate song "Stay (Just a Little Bit Longer)".
He has also noted that he kept playing so much of the first Modern Warfare that he forgot to eat, and when he tried to play 'a bit of the next mission' in XCOM: Enemy Unknown, he couldn't resist playing three entire missions before he could make himself stop.
In the episode "Towelie", the boys get the new game system "The Okama Gamesphere". They make up excuses to keep playing.
Stan: Uhh... we can't go to baseball practice because... Kyle has can't cancer.
In the episode "Make Love, Not Warcraft", the boys did nothing but play World of Warcraft for weeks, becoming incredibly fat and grotesque as a result.
This one is a double-example: they did all of this so that they could level up enough to beat someone who ALSO did this, literally having never once logged off since launch, and somehow had developed the ability to kill player characters, even when not flagged for PVP and on the same side no less. So what do they do once they achieve this godly status along with the Sword of 1000 Truths? Go back to playing the rest of the game like nothing happened...
This happened once to Lisa Simpson — she wasn't prepared for playing with a Crash BandicootCaptain Ersatz for whole week. She started playing when she was sick and didn't have anything else to do, but by the time she recovered she was hooked.
This happened to Hank in an episode of King of the Hill when he plays a GTA-esque game called "Pro-Pain". It's actually based on his life, being made by a couple of nerds.
During an episode of Brandy and Mr Whiskers, Brandy tried to keep Mr. Whiskers from pestering her by giving him a handheld game to keep his mind busy. He got so into it, that he was even worse than before.
A similar thing happened on Mike, Lu & Og episode "A Boy's Game", with Og getting addicted to a Bamboo TechnologyGame Boy that he made himself, even so far as to keep playing it even while a hurricane was destroying the island.
Doug wins a videogame system from a store, and then spending the next few days playing games while not doing his homework and nearly being late for school.