Carl Macek had to invent several of these when he made the multifarious Robotech. For example, Yellow Dancer is a singer who emulates Minmei.
This happens from time to time in One Piece, primarily through Usopp. When Usopp was first introduced he would regale Ill Girl Kaya with tales featuring things like a goldfish so large its poop was island sized, or claim he was sneaking around hunting a mole monster. After the Little Garden arc, the Straw Hats encountered a goldfish exactly like the one Usopp mentioned. During the Alabasta arc, Usopp faced Miss Merry Christmas, who had the power to transform into a mole-woman. The former case was lampshaded by Usopp commenting that the goldfish seemed familiar to him for some reason.
Also the time when Zoro had to defeat Mr. 1, who had the ability to compose his body to the hardness of steel. To learn how to cut steel and gain one step closer to defeating his rival Dracule Mihawk, he defeated Mr. 1. He then asked Zoro as he fainted if he plans on cutting diamond next. Mihawk himself in the war against Whitebeard tried to use his strongest sword slash to see the difference between the two, only to find it blocked by 3rd division commander Jozu, who turned his body into diamond.
During the anime's adaptation of the various Marine officers gathering in Marineford, Jonathan, The Chessmaster commander from the G8 filler arc, is shown arriving as well, accompanied by his subordinates Drake and Gu.
When Zoro makes his reappearance in Chapter 599 after training with Mihawk for two years, he makes his entrance by slicing a boat in two and mocking its inhabitants amongst the wreckage. Perhaps he gained more than just the man's skills in that time.
During the second season of Code Geass, Lelouch is shown walking past a wall in the school that is covered in cross-like marks, the end of the wall has blank bricks and a brick with just one line on it. This is a reference to the first season when he used his Geass on a girl with the instruction "make a mark on this wall every day" to test how long its effects last.
In Chrono Crusade, when Chrono tries to explain who the Pursuers are, he notes "If you count Leiraje, this is only the second time we've seen one!" (Leiraje was a character that had shown up in the first volume and kidnapped Azmaria.) Azmaria squeaks out "Really??" and Rosette snorts "Geez, nobody remembers him."
In the penultimate episode of Nichijou, the girls are confronted by a cop Mio had beaten up several episodes earlier. It turns out he remembered the incident and was about to bring them in, but lamented upon seeing that Mio had rescued a drowning child.
In the fifth episode of Princess Tutu, a lamp is possessed by a heart shard when she believes that she's been abandoned by the family she used to serve, and everyone has forgotten her. Princess Tutu told her that she was sure someone else would find her and love her for her light and warmth again, and sure enough, Ahiru takes the lamp home with her at the end of the episode. It's often seen in her room in later episodes.
This happens a few times in Yu-Gi-Oh! GX and 5D's, in particular referencing the original series. In GX a number of times, they reference a couple of the more famous battles outside of climactic showdowns, provided they were based on the manga at least, and occasionally referenced or alluded to well-known events or cards, like in episodes 18 & 19 where Judai dueled against a copycat who had stolen Yugi's deck. This occurs far-less often in 5D's, aside from the fact it's in what we used to know as Domino City, though there are a few allusions to icons of the past on some of the newer cards.
The Speed Fusion card portrays Dark Magician and Flame Swordsman fusing into Dark Flare Knight.
This happened plenty of times within the original series as well. The Pharaoh walking through a valley of lost spirits and flashing back to a bunch of minor antagonists. The cameos that Doma's swordsmen received after the Waking the Dragons arc, along with everyone else in the last few episodes of the whole show. While not free of filler, the franchise has a truckload of continuity nods.
Ayukawa, the school nurse in the GX anime, makes an appearance in the GX manga observing a student's coma and noting a similarity between that coma and events in the Battle City tournament, where four people fell unconscious after their duels (Mai, Jonouchi, Rishid and Bakura), and two of them were confirmed by witnesses to be the victims of sorcery (presumably Rishid and Jonouchi). She then promptly dismisses it all as nonsense.
Several aspects of Usagi and Seiya's meetings in Sailor Stars mirror Usagi and Mamoru's meetings in the first season of the series, culminating in Usagi confusing Seiya dressed in black and red for Tuxedo Mask, who wears a black and red outfit. (Seiya went as far as to throw a red rose to distract the enemy.)
Throughout Fullmetal Alchemist are scenes where you can recognize certain people traveling about — like the Curtises, Hohenheim, or a minor one, the mustached man in the white suit.
In Rush Valley, you also see automail stalls with photographs of their previous customers, like the man who hijacked the train in the first volume or the army guy in one of the spin-off games.
After Father Cornello outlives his usefulness, Lust lets Gluttony eat him. Later, Ed and Ling end up inside of his stomach and you can see a skeleton wearing some familiar garments.
The second-to-last episode of Best Student Council has basically every character that appeared in a single episode show up to act as a diversion.
Pokémon has a Continuity Nod in "A Lean Mean Team Rocket Machine", by having Jessie, James, and Meowth use their original Team Rocket motto.
Misty's Staryu makes its first appearance in "Clefairy and the Moonstone" and she calls it back before Ash catches up to her. In the next episode when she uses Staryu against him in a battle he checks it out on the Pokedex since he hasn't seen it yet.
Happens a lot in Monster. One notable instance is when Eva's flashbacks finally reveal why Tenma got back from his date in episode 4 so quickly.
Macross Frontier in particular is chock full of continuity nods: from Ranka singing songs of the previous installments to SMS formations being named after Fire Bomber songs.
Macross Zero had a retroactive continuity nod: after Sheryl Nome was revealed to be the granddaughter of Mao Nome, Sheryl's iconic Fold Quartz earrings were added to a shot in the Blu-Ray release of Zero to establish that they were a family heirloom.
In Digimon Adventure, Tai uses a set of cards to open a gate to earth while leaving out Agumon's card. In the followup series Adventure 02, Mr. Owikawa uses the same cards but leaves out the Gomamon card while including the Agumon card, sending him somewhere else entirely.
In the eighth episode after the battle with Ogremon and Leomon, Tai says to Agumon "two Digivolutions in one day, you must be exhausted". This refers to the previous episode which had Greymon battling Unimon, technically only a couple of hours earlier.
Quite often do characters in Pokémon Special make references to events that happened in the past, even if said events happened in another region. For example, when Byron learns that Platinum collected six badges in twenty days, he mentions that he heard of a trainer in Hoenn who collected eight badges in eighty days (ie, Sapphire).
At the start of the Platinum arc, when Platina meets up with Looker, one of the first things she asks is if he's supposed to get a free bike ride around Sandgem Park and if he's really a comedian, referencing the mix-up that occurred at the start of the Diamond and Pearl arc.
The fourth season of the Slayers anime aired in 2008; the ending sequence featured the plane chart noting the hierarchy of the five Mazoku lords, the four Dark Lords, and the Lord of Nightmares suspended in the background. The two spots on the chart reserved for the Mazoku Lords Fibrizo and Gaav are destroyed, nodding to the fact that they were both Killed Off for Real in the second season of the anime (which aired in 1996).
Oddly, in a possible case of potential discontinuity, the spot on the chart for Dark Lord Dugradigdu remains intact, despite having been destroyed in the third season (1997). It is considered Hajime Kanzaka's way of protesting the season, as it is the beginning of divergence from his books. Since then, he seems to have accepted the change.
In chapter 20 of Magical Girl Lyrical Nanoha Vivid, Vivio and her friends are given special bracelets designed by the TSAB Research Department that drains a person's physical and magical powers to help in their training. When Nanoha sees it, she makes a comment about how she used to do something like that when she was a kid, except she had to let Raising Heart manually do the draining for her since she didn't have something as convenient as the bracelets. This was a reference to Nanoha's Training from Hell regimen that was described way back in the first chapter of the Magical Girl Lyrical Nanoha A'ssupplementarymanga.
In the background of the earlier Haruhi episodes, nods to the original series could be seen in the background. Multiple events that weren't shown in the first season, but occurred in the novels, had their remainders shown in the club room. While most were later filled in on in their second season, unfamiliar fans may wonder why there is a frog costume or a bamboo plant lying around.
Daily Lives of High School Boys has a constant, but more subtle example in the manga: covers from a given chapter might portray the result or any aftermath from a event that happened in the previous chapter. This is often reproduced as the eyecatch after the skit corresponding to the said "previous chapter" in the anime adaptation.
In another example, in High School Boys and Seniority, Motoharu's sister's classmates came to their house for a sleepover and, among others, were quite interested to have Motoharu shaved. The eyecatch right after this skit was the manga eyecatch mentioned above, having the girls trying to forcibly shave Motoharu. The next skit High School Boys and the Saviour, we see Motoharu shaved and had a few Band-aids on his chin, clearly the result of being forcibly shaved by the girls.
Many scenes that were changed or added to the anime still borrow directly from other events featured or mentioned during the game.
A flashback detailing Chie and Yukiko's first meeting in episode 3.
Yukiko's pet bird in episode 4, hinted at during the opening cinematic of the game.
Adachi coming back from shopping at Junes with nothing but cabbage in episode 7
Rise's decision to quit being an idol in episode 9.
Personas and Shadows demonstrate abilities related to ones they have in the game.
Chie's shadow has her Persona Tomoe's weaknesses in episode 3.
Ara Mitama and Pyro Jack are strong against physical and fire attacks respectively in episode 4
Shadow Kanji's flunkies have the same immunities as they did in the game in episode 7. Also, Yamata-no-Orochi is fused with the same Arcana combination that would be used in the game. (Magician x Priestess = Moon)
During the battle with Shadow Naoto, when she turns Yosuke, Yu and Teddie into old people, she's actually using her Galgalim Eyes attack, which causes the Enervation status. The connection to the game is further established by having Kintoki-Douji use Energy Shower to reverse the effect - in the game, the skill Energy Shower cures the Enervation status effect.
Shadow Naoto also fights like she does in the game, by exploiting weaknesses. Yu keeps having to change Personas because she keeps preparing to use attacks that his current Persona is weak to (though thanks to Rise, Yu is one step ahead).
During the Shadow Naoto fight, Yu has Mot use Mudoon, which doesn't work. Naoto's Persona, Sukuna-Hikona, resists Dark attacks.
Fairy Tail is incredibly good at this, to the point that it's actually too much of an effort to list all the small background details in it, though special mention goes to the Continuity Porn that is Natsu's house and the manga's willingness to reference events from filler episodes of the anime.
In episode 30 of Legend of Galactic Heroes, the Flashback where Mittermeyer and Reuenthal saw Reinhard and Kircheis for the first time four years before the start of the series is depicted in greater detail in episode 6 of the Hundred Billion Stars, Hundred Billion Lights arc of the first Gaiden series, this time from the perspective of Reinhard and Kircheis (the animators made a minor Series Continuity Error in the first flashback though by illustrating Reinhard and Kircheis wearing their new rank insignias too early).