Examples of type 1 (characters involved in production)
A radio show on Fallout 3 featured "adventurer Herbert Dashwood and his stalwart ghoul manservant, Argyle." In each episode Herbert's bumbling landed them in situations Argyle would singlehandedly extract them from. The player could meet Herbert in game, who claimed he wasn't really that big of a fool but admitted Argyle was most certainly a badass. You can find Argyl's corpse in Rockopolis. He fell trying to escape from the slavers, (which Dashwood accidentally led to Rockopolis) and the population of Rockopolis which Dashwood barely escaped from, the news of which will crush Dashwood.
GTA Radio in various games features radio programming, including talk radio and news.
Grand Theft Auto IV features television programmes that can be watched, including complete episodes of in-game series Republican Space Rangers, The Serrated Edge, Princess Robot Bubblegum (In Episodes from Liberty City) and a history of Liberty City. The Men's Room is a talk show matching a Camp Gay host with MMA legend Bas Rutten.
Saints Row 2 has FUZZ, a violent parody of Cops where players impersonate a police officer and apprehend criminals in excessively violent ways (chasing down a streaker with a flamethrower, to name one example).
In the Ratchet & Clank series for the PlayStation, Clank comes to star in a James Bond-like series called Secret Agent Clank. (Ratchet is consigned to the role of Agent Clank's bumbling chauffeur, to his annoyance.) In the appropriately titled PSP game Secret Agent Clank, Clank actually assumes his television identity to help clear Ratchet when the latter is framed for a crime.
In the games preceding it, Captain Qwark also has his own show and considerable celebrity although he sold out to the Big Bad to get it.
The setting for the start of the game Final Fantasy IX revolves around the theater troupe Tantalus performing a play called I Want to be Your Canary (Queen Brahme's favourite) for the birthday of Garnet, princess of Alexandria. In actuality, the performance is merely a front, for Regent Cid of Lindblum's order to 'kidnap' Garnet (who, ironically, wanted to run away, anyway).
Likewise, Final Fantasy VI had the famous opera scene, where the mother of all contrived coincidences leads to Celes having to play in an opera. It tells something about the skill of everyone involved in that scene that many gamers were moved by the events of the opera, which are fictional even within the fiction they're currently following.
Also in Final Fantasy VII, Cloud and Aeris(or Tifa or Yuffie, depending on how you play the game — though the scene is just outright skipped if you're with Barret) get to play pivotal roles in a brief play during the Gold Saucer segment.
The relevance of the play "Loveless" in Crisis Core
Night Springs in Alan Wake, an obvious pastiche of The Twilight Zone, which Alan wrote a few episodes of before writing novels, as his manager Barry later mentions. It fits type two as well, as Alan gets to watch the show on certain TV sets during the course of the game.
We also get to read two pages from Alan's most recent novel, The Sudden Stop, a reference to Remedy's earlier Max Payne games. The pages are even written in Max's Private Eye Monologue style and read by his voice actor.
Super Mario Galaxy has Rosalina tell a very sad story about a young girl having to deal with the loss of her family. The girl in the storybook is actually Rosalina herself.
Mortal Kombat: None of Johnny Cage's movies where actually shown in the game, but plenty were mentioned. A few notable ones were Dragon Fist (which had two sequels), HWAAAAA!! (which won an Oscar, according to Deadly Alliance), Sudden Violence (supposedly award-winning), and Ninja Mime, which was a box-office flop in America; Cyrax loathed this one. He also supposedly stared in movies that were based on his experiences in the first two games of the franchise and Deadly Alliance. (The last one appeared to be his greatest success as an actor, but unfortunately, only existed in his non-cannon ending to that game.)
In the bonus rounds of Sonic the Hedgehog Spinball, Sonic operates an actual pinball machine, in what looks like Las Vegas. You can see his reflection in the glass, and his eyes and hands even move as you play.
The Sakura Wars games are loaded with these, because of the entire cast's cover identities as part of a theater troupe. In addition to the many, many stage productions they put on, there are also the movies made by the studios owned by Sumire's family (including the infamous Crimson Lizard), and the radio serial Red Lad.
Tokyo Mirage Sessions #FE follows a casting agency, making this a given. Productions in which the party members are involved in include but are not limited to Microwavin' with Mamorin and Sneeze Detective Maho.
Splatoon has Inkopolis News, a news show hosted by the Squid Sisters, Callie and Marie. Its primary purpose is to report which battle stages are currently available on the online modes, as well as information on the Splatfest events. When you start the game for the first time, the duo will also report on the disappearance of the Great Zapfish, a crucial plot point in the game's story mode. Upon clearing the game for the first time, a news segment plays reporting the return of the Great Zapfish.
Travis Touchdown's favorite anime in No More Heroes is Pure White Lover Bizarre Jelly, which appears to be a Magical Girl Mecha series. We never see the show itself, but he has a T-shirt with the main characters on it (and more can be bought), there are posters of it all over his motel room (including one that he presses to and sighs, Moe~), he seems to have stolen his attack names from it, and he plays an upward-scrolling SHMUP based on the series to pass the time on the subway on his way to one of the game's boss encounters.
Suda51 has expressed a little interest in Defictionalization of the show if the opportunity comes up. Presumably it would be a scathing parody of anime tropes... or just plain Mind Screw. Or both.
The Max Payne series features shows like the cartoon Captain BaseballBat-Boy, the psychological thriller Address Unknown, the costume drama/soap opera Lords and Ladies, and a blaxploitation send-up of Max Payne called Dick Justice.
Sam & Max Save The World features a variety of shows from WarpTV, including the sitcom Midtown Cowboys, talk show Myra!, and celebrity tell-all program Oh, Is He Still Alive?. Turn into Type 1 when the two protagonists get embroiled in them in "Situation: Comedy".
In the Harvest Moon series, there are often shows that one can watch on the TV in their farm-house, in addition to weather and news channels.
Mario Party Advance has a show called Toad Force V, which is about a robotic Toad named Jack and his partner, the heroine Britney, who is more popular. Together, they fight villains such as the Spore King and Toxic Toad Z. The show is so extremely popular that there are a few quests related to this show. It is also mentioned several times in the game.
In the Pokémon games, there are several shows that can be watched on the TVs, in NPCs houses.
From Pokémon Gold and Silver onwards, you can listen to radio shows on the Pokégear, including one from Professor Oak.
The Deb of Night in Vampire: The Masquerade – Bloodlines gets a special mention for being a radio show within a video game. You can hear it on any radio you find in the game, which plays pre-recorded dialogues (which ones, depends on how far your progressed with the main quest) between the hostess Deb and people who call her.
Tokimeki Memorial 2 is the host of several Shows Within a Show: "Super Dragon Warrior" (Chou Senshi Dragon, a Hot-BloodedSuper Sentai series), "Go-Driller" (a Hot-BloodedSuper Robot anime), "Space Idol Love-Love Star" (Uchuu Idol Love-Love Star, a Magical Girl series), and "Protuding-navel Kero Kero" (Kero Kero Debeso, an anime). Homura Akai is a big fan of the first two, to the point of mimicing the Dragon Warrior's special kick and wielding drills just like Go-Driller ; Mei Ijuin likes the second too ; Miyuki Kotobuki is an avid fan of the third ; and Miho Shirayuki adores the fourth.
This overlaps with Type 3, as "Go-Driller" and "Space Idol Love-Love Star" become plot points in the storylines of the Substories games Leaping School Festival and Dancing Summer Vacation respectively.
In Super Robot Wars Alpha, Ryusei Date is fan of mech simulator game call Burning PT, which is actually used by military to recruit pilot. It's only mention in dialogue and players never actually see the game until anime adaption of Super Robot Wars Original Generation though. In the end of Super Robot Wars Original Generation Gaiden, he end up watching his favourite anime Banblade with his Unwanted Harem, but players never actually see how the anime look like. Also in Super Robot Wars Alpha 3, he give Mylene Jenius a rare copy of Macross: Legend of Lyn Minmei as birthday present.
Some of the Grand Theft Auto games have a number of different (all rather raunchy) shows that the player can watch.
In Skullgirls, Peacock and Parasoul (secretly) are fans of the kid's show Annie: Girl of the Stars.
Pritchard from Deus Ex: Human Revolution appears to be a fan of Final Fantasy XXVII (the franchise exists, but the actual game doesn't), and has a poster of the main character (some kind of Black Magician Girl, from the looks of it) in his office.
In the Team Fortress 2 comic "Ring of Fired", The Demoman and his possessed ghost sword, the Eyelander, are watching a show called Ghost D.A. It's hilariously bad, from the protagonist being a prosecutor, not a defense attorney, to the cliche dialogue, to the fact that he phases out with a "doodily doodily doot" noise. The two of them (especially Eyelander, who has developed its ability to speak, and has become a Cluster F-Bomb) comment on how awful and inaccurate it is.
Attack of the Friday Monsters features a kaiju show that is filmed in the protagonist's hometown. The protagonist and his friends are fans of the show, and you have to play the tie-in card game to advance the plot at some points. The protagonist's next-door neighbour is a scriptwriter for the show, and you can visit the studio and talk to the producer (type 1).
Undertale: Alphys is a huge fan of Mew Mew Kissy Cutie, an anime, though she doesn't like the sequel. Said anime is only discussed, however.
Stardew Valley has Legend of the Prairie King, a top-down shooter that's fully playable from the Stardrop Saloon. There's also a co-op mode, though it's only played during a relationship event with Abigail.
A major point of Assassin's Creed I is that you are playing as Desmond Miles, who spends most of his time in the game participating in an interactive simulation of his ancestor's memories. In other words, Desmond is playing a video game.
Every other Assassin's Creed game turns out to work exactly like that, sooner or later. Sometimes Desmond is the one living through the simulation, at least one time it's one other guy who is later revealed to have died, and in Black Flag it's you!
Final Fantasy VII Crisis Core has both the book and the play version of Loveless, which has already been established as a play in the original game. Resident Villain Sue Genesis is a huge fan of the book, to the point of basing his rebellion around it and wandering dangerously close to having Otakukin type thoughts regarding he and his friends reliving the story. In an interesting case of Truth in Video Games, the player can meet up with fans of the book who complain about the Adaptation Decay and Misaimed Fandom of the play version.
Saints Row 3 and 4 (in addition to the Nyteblade show in type 2 example), gives us Professor Genki's Super Ethical Reality Climax, which is an example of types 1, 2, 3, and arguably 4 all rolled into one. Professor Genki is the host/mascot the show, itself is a Japanese game show similar to Takeshi's Castle but with firearms and various mascots trying to kill the contestants as they try to get through a colorful, bizarre obstacle course before the timer runs out. The Saints are fans of the show (type 2), and participation is a gang activity which increases control over Steel port...somehow (type 1), with an entire expansion pack devoted to a Superbowl-esque event in which the Saints Boss participates (types 1 and 3), and, finally, the general bloody antics and anarchy the player gets up to is roughly similar to the regular gameplay, and way past 11 (type 4).
Pony Island: The titular Pony Island is loaded onto an arcade machine located in Limbo.
The Lakeview Cabin Collection is actually a series of films, with the original Lakeview Cabin apparently being the first installment. The Hub Level is a movie theater, with pedestrians walking to view the movies. You're still not entirely safe, by the way.
One advertisement on the Citadel is for a film, Citadel, based on the events of the first game. Unlike many of the above examples, there is no eeriness to this - most of the events of the first game are public knowledge.
In the Max Payne series, Dick Justice is a Self-Parody of the first game. Address Unknown is eerily close enough Max Payne's story to feed his paranoia and guilt over the death of his wife; although he avoids making the association to himself in waking monologue, it does haunt his dreams.
META is a game about editing the game "Awesmoe [sic] Quest", so the latter is a game-within-a-game.
Examples encompassing multiple types
Persona has recurring Sentai series Phoenix Ranger Featherman, first introduced in Persona 2 as Phoenix Ranger Featherman R.
In Persona 2: Innocent Sin, the Masked Circle cult turns out to be a corrupted version of a Featherman-inspired children's group. Specifically, the very same group formed by the main characters when they themselves were little kids.
In Persona 4, several party members admit to having been Featherman fans as children, with Naoto's own dungeon stated to be similar to several of the show's secret bases. It's also referenced in the Temperance Social Link, since Eri Minami's son Yuuta is a big fan.