Every episode of everything by Chuck Lorre Productions. He uses his Vanity Plate like a blog (making the concept of blogging Older Than The Internet). And if you miss it, you can always find the archive on his site.
24: In the first season finale, as Nina Myers attempts to escape CTU after being exposed and covers her tracks, some pictures of the cast and crew are shown.
Agents of S.H.I.E.L.D.: In the episode "The Well," the online message board of a neo-paganist hate group is shown for about a second. If you pause it and read the messages, you'll notice that one is amusingly off-topic.
In the pilot movie "The Gathering", an assassin scans his hand to enter the quarters of a tech smuggler. Some fans with lucid freeze-frames on their VCRs noticed that the authorization message read, "Laurel Takashima cleared". This hinted at a plot in the planned arc in which it would turn out that Laurel Takashima, the executive officer of Babylon 5, was a mole from a hostile force. Unfortunately, between the pilot and the series, the character of Laurel Takashima was Put on a Bus and her planned plots divided between other characters.
In the episode "And Now For a Word", a commercial for Psi-Corps has the line "The Corps is your friend, trust the Corps" flash for a brief moment.
Buffy the Vampire Slayer: At the end of the episode "Out Of Sight, Out Of Mind", a character is seen in a classroom opening up a book which is supposed to be about assassination techniques. The page is shown just long enough for the audience to parse a more on-topic chapter heading, but most of the other text consists of the lyrics to "Happiness Is A Warm Gun".
In the second-season episode "Aerodynamics of Gender", Abed imagines himself as RoboCop with a first-person heads-up display. Reading the margins of the screen shows Abed reminding himself to record Cougar Town, keeping a running synopsis of the episode, and tracking the female characters' monthly cycles!
In a Criminal Minds episode, criminals are hiding their activities by listing fake business names in their appointment books that are all named for video game characters. There's one more than the names spoken out loud by the characters: you can briefly see one of the appointment books with "Ezio's Flower Shop" listed on it.
The spaceship in "Robots of Sherwood" has an image of Patrick Troughton as Robin Hood as part of its database on the character.
ER: The names of patients on the wall behind the nurses' station were actually that of various crew members and occasionally the real life names of the cast. Then, in the final season, as several doctors prepared to leave, they were taken down to basement to put their name plates on the wall. On closer look, indeed, the names of every doctor/nurse who had left the staff/cast by whatever means was present (making this a nice Continuity Nod as well)).
Friends: In "The One After the Super Bowl" (Part II) when Ross' monkey Marcel cannot meet him at his apartment he goes out to eat with Joey and Chandler, the bonus is on the menus of the restaurant that say Marcel's on them.
Fringe: Americans in the alternative universe have identity cards. Freeze-framing Alt-Broyles's card in Season Four shows that they have dates in the Anglo-European DD-MM-YY format instead of the US MM-DD-YY format.
Game of Thrones: The book Ned consults to discover the true parentage of Robert Baratheon's children has a page listing several members of House Targaryen mentioned in the novels: there's King Viserys II, King Aegon IV, Queen Naerys, Princess Daena the Defiant, King Daeron II, Queen Myriah Martell, Princess Daenerys (GOT Daenerys' namesake), Prince Baelor, King Aerys I, Prince Rhaegel, Prince Maekar and even the Blackfyres: Daemon, Aegon, Aemon and Daemon II.
The White Book of the Kingsguard. For show-only viewers, this book makes the first reference to a very important event in the backstory, concerning Robert's Rebellion: the fight at the Tower of Joy, where Ned Stark and Howland Reed killed three members of the Kingsguard and ultimately, his sister Lyanna died.
Glee: In the season 1 episode "Hairography", Quinn Fabray and Noah "Puck" Puckerman get into a fight over the fact that Puck was sexting Santana Lopez during a babysitting gig with Quinn. The freeze-frame◊ of Quinn searching his phone for evidence reveals that Puck might be the worse sexter ever; one sent message features the creative and eloquent line, "You so hot and stuff and stuff."
Good Luck Charlie: The chalkboard on the fridge has a section for chores, as well as sections for each Duncan, even Charlie. If it's visible, expect it to at least vaguely be in the episode and most of the time a huge part of the episode.
Heroes was very good at this in the first have of S1, with tons of stuff in each episode. For instance, Suresh's map with color strings. There was bits of Foreshadowing regarding upcoming characters as early as the first episode. The folders in Old Suresh's file cabinet are labelled with the names of powers featured in later episodes. During the second half there was considerably less of this and in later seasons these little clues appear to be largely absent.
Home Improvement had "Watch Tool Time" flash quickly several times in the intro of later seasons, when the cast members were shown on screen. A screenshot of this can be found here.
Horrible Histories: When George IV is first mentioned in the refrain during the Kings and Queens song, he can for a second be seen pointing to himself in an Attention Whore manner.
There are also plenty in the "historical character uses the internet" sketches. For example, Cleopatra getting a mail from her sister and Henry VIII's mistress Bessie Blount being on his top 8 on Yebo.
In the episode "Rebels," Detective Curtis is reading a BBS posting about a murder in a bar. For a brief moment, Curtis's computer screen is visible. The email is the same paragraph repeated twice, followed by an extended rant by the prop guy, who wonders if he's filled up a screen yet with his nonsensical ramblings. Also, the email gets the name of the bar wrong.
Appearances by Jacob, the beechcraft in the corner of Charlie's dream, changing picture frames, briefly seen documents in the hatches.... Most notably, the Blast Door Map which, while only visible for several seconds, contains numerous references to future plot points, such as The Flame, Magnus Hanso as the captain of the Black Rock, the date of the Incident etc.
Once in a while, though, something the creators intended as a joke was noticed and overanalyzed to death by crazy fans, like the Dharma Shark, who was then jokingly named "Ezra James Sharkington" by Damon Lindelof and Carlton Cuse, and popped back up in a sixth-season episode, presumably as a Shout-Out to said crazy fans.
The Mentalist: The episode "Seeing Red" briefly flashed a computers screen showing the charitable contributions of a wealthy murder victim. She wrote checks for "Organization for the fight to end Women's Suffrage", "Society for Teaching English to Americans", and "P.A.N.I.C. (People Against Namining Infants Chad)".
Modern Family: In Connection Lost, in The Stinger Claire quickly scans over the first sentence of Alex's college admissions essay before giving up and just texting her that she loved it. If you pause long enough to read the actual essay visible on the screen, one sentence has "I know you're not reading this, mom" inserted in it.
In Newswipe, there's a bit where a list of the G20 bodies scroll across the screen, too fast to read. Slowing it down reveals that it says "..SPAIN THE NETHERLANDS THE NEW PARTNERSHIP FOR AFRICA'S DEVELOPMENT BOTTOM LAND NO NOT REALLY WE MADE THAT ONE UP AND YOU BOTHERED TO PAUSE THIS TO READ THE PHRASE "BOTTOM LAND" WHAT A DISMAL LITTLE PRICK YOU ARE THE ASSOCIATION OF SOUTH EAST ASIAN NATIONS THE EUROPEAN COMMISSION..."
An episode of The Outer Limits (1995) features an old Holocaust survivor who occasionally remembers the horrible day that his young daughter was dragged off by camp guards, never to be seen again. Looking closely during those flashbacks, one can see that the "guards" are actually the survivor's adult son and a time traveler from the further into the future. In the episode's climax, the pair have traveled back in time as part of a plan to bring one of the camp guards to justice; the survivor's son made a spur of the moment decision to rescue his half-sister by bringing her back to the future.
At the end of episode 3 ("No Quarter"), Maggie's iPhone reactivates thanks to the power-activating pendant, and the lock screen shows the date as Monday, September 17 - the date of the show's premiere in 2012.
There are several newspapers shown throughout the series, each with relevant articles in them. The most hilarious are the article◊ revealing why Sherlock was kicked out of the courtroom in Reichenbach Fall and the various newspapers◊ Janine brings to the hospital in His Last Vow.
Lexmas: A lot of fans apparently wondered what dream Lex did to get a humanitarian award, but a simple freeze frame would reveal it is work for the homeless as stated on the certificate.
Abyss: As Brainiac starts to delete Chloe's memories of Clark, she begins to have a flashback to the Dark Thursday kiss before the image of Clark is pulled away from her, interspersed with flashes of a white Superman symbol.
Salvation: Clark wearing the traditional Superman suit could be seen briefly as a reflection in the Daily Planet globe. There are even briefer frame of Superman flying pass the camera and a flash of the Superman symbol as the vision ends.
Ships' dedication plaques were especially fond of it. Each one would have a list of senior officers (usually members of the production staff) and a ship's motto that was usually a Shout-Out of some kind or another.
Touched by an Angel: At the conclusion of an episode in which the angels were trying to aid a detective who specialized in missing children's cases, one of the cast members revealed that the numerous "Missing" posters seen in the background throughout the episode were in fact those of real missing children. Pausing the footage allowed the viewer to get a much closer looks at the details present.
Trailer Park Boys: In one episode, a character reads a written note aloud as the camera focuses on it. After he is done, the camera pans down slightly for a split second to reveal extra text, which says "If you're freeze-framing this on DVD, you're fucked!"
The Vampire Diaries: Stefan is calling Isabel and on his phone you see a number, a real number, 919-399-2507. If you call it you get audio of Katherine, Stefan, and Damon talking about Klaus and who to trust.
Intentionally invoked on Letterman. During a viewer mail segment, Dave read a letter from a guy who said he recorded the show and watched it later. Often, there would be a quick shot of the cue-card boy, and the viewer would pause the tape, and read the joke before Dave told it. When Dave finished reading the letter, there was a quick shot of the cue-card boy holding a nasty note for the guy that wrote the letter. For the lulz.