In FLCL, we have Gaku (a.k.a. Mr. SMOOOOOOOCH~!) and Masaki, two Odd Couple/ Red Oni, Blue Oni classmates of Naota who, when they show up, also serve the unique dual-role purpose of being the Greek Chorus, as they comment on the truly bizarre events of the series.
Mazinger Z: In this series and the sequel we have Nuke and Mucha, best friends and tag-alongs of The Rival and Butt Monkey Boss long before the start of the series. Before meeting and befriending Kouji Kabuto they were two average, ordinary high-school students, but after meeting him their daily life includes battles between Humongous Mechas, fighting or fleeing from armies of Mooks, sneaking into enemy secret bases and basically surviving. Often they get -unwillingly- dragged -by Boss- in Kouji's adventures, and they provide with the rational counterpoint -and lampshading- to any stupid stunt Boss has come up with. Later in the series Boss got himself a Made Of Junk Humongous Mecha and required that they helped him to pilot it -much to their chagrin-. In Great Mazinger their situation did not get more normal, that with the monsters from Beneath the Earth invading the surface world bit and Boss demanding they help him to fight them like part of an absolutely helpless plan to woo Tsundere Jun Hono -Love Interest of The Hero Tetsuya, whom Boss can not stand-. In other series (Mazinkaiser, Shin Mazinger, Shin Mazinger Zero) of the Mazinger franchise they are given the same role.
Those Two Guys are never seen on screen in Revolutionary Girl Utena but still manage to get a lot of focus, and even cosplayers. All the audience ever sees of them is their shadows projected onto a wall as they act out bizarre skits that are a commentary on what's happening in a particular episode.
Kyon's two friends Taniguchi and Kunikida from Suzumiya Haruhi. One's tall and lecherous, the other's baby-faced and timid. Taniguchi wound up being a sort of Ensemble Dark Horse after getting a few good scenes (and an Image Song CD for the second season), while poor Kunikida is just kinda there.
Taniguchi actually serves a significant function in the novels and the anime — he's the one non-SOS Brigade character that has the most important interactions with Kyon. His role is in fact similar to Koizumi's, in that he continuously confronts Kyon with all sorts of uncomfortable facts; and because of this, he is, along with Itsuki, the biggest recipient of Kyon's Obfuscating Stupidity. This comes out more than anywhere else in "Sigh".
Ranma ½ has two sets of these: Ranma's friends Hiroshi and Daisuke, and Akane's friends Yuka and Sayuri. They're also basically the only people without overly complicated Meaningful Names, just very common ones, indicating how normal they're supposed to be. In the original manga, they didn't even have names.
Technically, Akane has four female friends gravitating around her, both in the anime and the manga. Yuka and Sayuri are just the most prominent — semi-fanonical names for the other two: Asami and Hiroko. They tends to often comes in pair, though, fitting the trope most of the time. Nabiki also has her two cronies, seen mostly in the anime.
Komatsu and Hatta from Kimagure Orange Road are a standard indistinguishable perverted pair of best friends of the main character Kyousuke.
Keigo and Mizuiro from Bleach. At one point it looked like a subversion was coming up in the pipeline, as the local Trickster Mentor Urahara mysteriously told them that it was time for them to get involved near the beginning of one arc... but no sign of this appeared, other than Those Two Guys saying hi to the big bad briefly.
Keigo is a strange case, as while he isn't directly involved with Ichigo or the Soul Society, he is actually able to see spirits and has interacted with certain Soul Reapers.
Earlier in the series, Orihime and Tatsuki filled these roles, although Tatsuki got into the supporting cast, and Orihime is now a regular, in fact she's the whole motivation for the Hueco Mundo arc.
Although they aren't seen together (some people would love if that happened), Chizuru Honshou and Ryou Kunieda seems to apply to the female part of the trope, at least in the manga continuity, where they are the two most active females from the human background cast.
We also have the other two girls in Orihime, Chizuru and Tatsuki's group of friends, Mahana and Michiru.
Don't forget Kiyone and Sentaro, Captain Ukitake's co-third seats, who he has in place of a lieutenant. Loyal, enthusiastic (Kiyone fangirls 'her' captain), not entirely competent.
Jubei-chan has two sets of these, of both sexes — Maruyama Shoko & Sachi Toyama are Those Two Girls for Jiyu, and Kozaru & Ozaru are Those Two Guys for Ban.
In Azumanga Daioh, Chiyo's two friends, Miruchi and Yuka, from before she was sent up several grades, looked like miniature versions of the two main female teachers. They even have similar names: Yuka looks like Yukari, and Miruchi looks like Minamo, a.k.a. Nyamo.
There was also a That One Girl in the class: Chihiro, who had a grand total of one memorable scene. When another ordinary student was needed, it was usually Kaorin.
There were also Two Guys who had speaking roles in the first episode and then were barely ever seen again. Only one was given a name (Masaaki Ohyama). The other's main attribute was looking like a male version of Nyamo.
Haitani and Shirai in Love Hina. The pair is so mundane that Keitaro and the other characters routinely forget who they are. Lampshaded, as both seem frustratedly aware of this.
Kouta and Haruhiko from Nyan Koi!. The latter is an otaku who regularly lampshades the harem elements going on around Junpei.
Touji and Kensuke from Neon Genesis Evangelion, perhaps the first real friends the main character got. However Touji suffers a severe injury from getting involved in Shinji's lifestyle, and both disappear by the end of the series because Tokyo 3 gets evacuated and they have to move away.
Along with Class Representative Hikari, they're often the comic relief trio in spin-offs, sequels, fanfiction, etc.
Misao and Ayano from Lucky Star. At one point, Misao even bemoans that she and Ayano are essentially part of the background, completed with them suddenly turning into watercolor still versions of themselves.
However, just like what happened with Taniguchi and Kunikida above, Misao has become an Ensemble Dark Horse of sorts, even getting her own solo character song album. No such luck for Ayano, though.
Ayano now has an image song..But so does basically everyone else.
Heck, don't forget their official label, "Haikei (Background) Combination."
Kyouko and Ryouko are Meimi's, but Asuka Jr. also has his own pair, Yasuhiro and Chiba, whose names aren't used onscreen until episode 39. Keep in mind that the anime is 43 episodes long.
Each of the Knights in Magic Knight Rayearth has her own backup duo, with whom she becomes more and more estranged.
Alisa and Suzuka from Magical Girl Lyrical Nanoha. Alisa had a much bigger role in the Triangle Heart universe, but she was jaded, traumatized and undead, though her current incarnation keeps insisting on involvement in the action.
Subverted in ViVid. Rio and Corona start the series looking like Vivio's versions of Suzuka and Arisa, but then we find out that they're both mages, and pretty damn good ones too.
Colin and Mary in Soukou No Strain looked completely set up for this role... until they died in the first episode.
Honda/Tristan and Otogi/Duke in Yu-Gi-Oh! fit this role later on in the series. In the original manga, Jounouchi/Joey and Honda were 'those two guys' who still got to do something cool and useful once and a while, but as Jonouchi became one of the main secondary characters in the duel monsters arcs, Honda was demoted to being a cheerleader for the most part. He often ends up together with Otogi during the scenes that don't focus on ancient Egyptian prophecies and children's card games.
We have also Insector Haga (Weevil) and Dinosaur Ryuusaki (Rex), who started as kinda-villains then faded into has-been background characters. However, when it comes to Yu-Gi-Oh!, they are about as normal as anyone ever is.
Asuka's friends Junko and Momoe in Yu-Gi-Oh! GX. Their main purpose seems to be falling madly in love with every handsome dude in the school (especially Manjyome, Fubuki, and Edo).
Digiko's two otaku from Di Gi Charat are essentially this... except that they're saddled with the unfortunate but memorable collective nickname "Bukimi" (literally "Creepy" or "Eerie").
In Digimon Tamers, Takato's friends, Kazu/Kenta, and Jeri/Juri. At least, at first. Instead of fading, they're brought into the mix eventually. (Now, Kazu/Kenta and Jeri each have a set of three friends who will fill that role.)
In InuYasha, Kagome's friends from school (Yuka, Eri, and Ayumi in the anime and unnamed in the manga) who try to help Kagome sort out her romantic entanglements — blissfully thinking she's dating a delinquent when in fact she's hanging out with a half-dog-demon.
Also, anytime Koga showed up, he would invariably be followed by his two lovable lieutenants, Ginta and Hakkaku — or, in one memorable instance, preceded by them, as they hunted down Inu-Yasha as the only person they could think of who could beat some sense into their packleader while Koga was being mind-controlled by Big BadMagnificent Bastard Naraku.
Tamiya and Otaki, the heads of the Nekomi Tech Motor Club, from Ah! My Goddess; in a mild subversion of the trope, both of these characters actually manage to take the spotlight from time to time in the manga, though this is less true in the anime series.
Suzuki and Sato, the heads of the Photography Club, from Ai Yori Aoshi.
Naru Osaka and Umino Gurio from Sailor Moon, Usagi's classmates. Featuring quite prominently in the first season, they become less and less important over the course of the series and have disappeared by the last season. It's even worse in the manga, where they disappear almost immediately: as soon as Ami appears, they're gone.
In the anime, we also had Usagi and Naru's classmates Yumiko and Kuri. They stick around for some episodes of the first series and then disappear.
YuYu Hakusho; Kuwabara's gang. Keiko also has two friends who hang out with her in the first story arc.
Hilariously lampshaded in Happy Lesson, where Those Two Guys introduce themselves and are listed in the credits as Student B and Student C, complete with romaji letters showing which one's which on their forehead. They primarily spend time harassing the class president, who they swear is the leader of their trio (hence 'B' and 'C').
Though they do visit the gravesite of "Student A".
Drake and Ted from FAKE. Subverted in FAKE II with their promotion to the Five-Man Band.
Poor Rivalz from Code Geass is That One Guy, who goes out of his way to try and do something cool and noble in the season finale... and fails. The Japanese fans nicknamed him "Air", an effective description of how relevant the poor guy actually is to the main plot.
Taro, Myu-myu and the other guy from Serial Experiments Lain, often seen hanging out at the Cyberia or somewhere like that; Taro does gets some protagonism though, telling Lain what the Psyche processor is for, and then having a one-scene affair with her.
They are more a plot-device than Those Two Guys. The series also has a straight example, namely Juri and Reika, Lain's only school acquaintances/friends apart from Arisu. Reika is outspoken, while Juri is kinda childish, for example suggesting that Arisu should date a boy for the sole reason that people wouldn't make rumours about her crush towards a teacher. Neither of the two ever learn about the massive, terrible phenomenon going on right under their noses, even when Juri was the one who first alluded to it in-series (she was seen crying her heart out after receiving an e-mail from Chisa Yomoda, who had just killed herself.. right after Chisa's death).
Shiratori's three art school classmates in Mahoraba, two girls and one guy, are so ordinary they don't even get get named until the final chapter. One of the Drama CDs revolves around trying to find their names.
Osamu Tezuka had the same two guys in nearly ever manga he did, a pair named Tic Lamune and Tucker Calpis who were deliberately designed to resemble Abbott And Costello. Tamao, Ken and Shibugaki, the boys from Astro Boy's class, also fit the bill.
In the Hayate the Combat Butler anime, no less than five girls from the Absurdly Powerful Student Council fit into this category. Three of them — Hanabishi Miki, Segawa Izumi, and Asakaze Risa — are more regular in anime appearances and are very rarely found apart. Aika and Chiharu appear much less in the anime and they lampshade this in one episode.
In the first season, it's mostly because Aika and Chiharu hadn't yet even been introduced officially.
Chiharu has gotten a much improved role more recently and Aika has been given foreshadowing for becoming much more important, the trio don't even seem to be interested in gaining any more focus.
Tuk and Mok in Kemono no Souja Erin qualify, although they do get a day in the limelight ep in episode 25.
In a somewhat unorthodox example, Li Syaoran of Cardcaptor Sakura managed to be both the straight man in a Those Two Guys combo (his partner is Yamazaki), a major recurring character and the Love Interest.
And when Eriol appears, he takes Syaoran's role of the straight man in his duo with Yamazaki.
Yamazaki and Chiharu, a male and female pair, fit into the more standard Those Two Guys roles, although they're much more memorable than most, specifically amongst Sakura and Syaoran's group of friends.
Yuki and Toya could qualify to a certain degree. They subvert it later, though, when it turns out that both of them (Yuki, or should I say Yue, in particular) are very involved in the plot indeed.
Those two guys from Fruits Basket. They are literally so unimportant to the main plot that the poor guys aren't even given names, despite them showing up various times, mostly to make fun of Kyo.
Izumo and Kotetsu from Naruto. Up until their involvement in the fight against Hidan and Kakuzu, they were always the ninja Those Two Guys, even to the point of remaining unnamed in the manga through multiple character popularity polls.
Additionally, Homura and Koharu, the two village elders, seem to be pretty inseparable. Although they work together as the only two members of the Konoha Council, which demands that they spend time together, they are never seen apart from one another. However, it is later revealed that they, along with Danzo, orchestrated the Uchiha Clan massacre.
The two girls in Amu's class in Shugo Chara!. One wears glasses and the other, who is later revealed to be named Manami, wears her hair in two buns.
Toradora has Noto and Haruta, as well as Those Two Girls Kihara and Kashii.
Subverted: They all become more significant later on.
Yamanaka and Iwashima generally serve this role in Gash Bell, although Iwashima's U.F.O. obsession often goes into weird places.
Drafted basketball players Satake and Yamaoka of Eyeshield 21, who mostly show up to remind readers that yes, the Devil Bats do have enough players for a full football team. On one hand you have the basketball volunteers who are only there to hit on the Cute Sports Club Manager and play it as a straight as can be (their only relevant scene was in the third chapter). On the other hand you have Ishimaru, whom which the series and the characters never fail to acknowledge as "boring and insignificant", to the point that those qualities actually make him memorable and important to the team (everyone forgets to block him).
Also, Muro and Miyake from the soccer team periodically show up to be obnoxious and end up humiliated for their effort.
Keroro Gunsou has Natsumi's classmates Yayoi and Satsuki, who actually come very close to discovering the Keronians' existence on several occasions.
Maria Ross and Denny Brosh seem headed this way at the beginning of Fullmetal Alchemist, but then Ross gets unpredictably swept away by the plot and Denny is left to fend for himself as that one guy. He and Maria do remain as Those Two Guys in the 2003 anime.
Gokinjo Monogatari has Pii-chan on Mikako's friends' side, and Jiro on Tsutomu's. They never get an important role because Pii-chan is apparently just an excuse for Yazawa to draw sweet lolita outfits due to Author Appeal, and Jiro is always busy with his part-time jobs.
Yoland and the other guy from Mobile Suit Gundam Seed Destiny.
Kimi ni Todoke's own Hirano and Endo tend to just stand around, occasionally commenting on the situation at hand. Other than that, though, they usually blend into the crowd, especially in the manga.
Harvar and Ox from Soul Eater, although this is a subversion in that the manga actually increases their roles alongside other pair Kim and Jackie, which formed a subplot for the recent arc. Though none of them possess the unusual qualities of Maka's team, they are more than capable meisters and Weapons, earning the two-star rank alongside the that group.
Now they're all part of Spartoi and playing some role in tracking down Noah and Medusa. Cue rather awesome moment with Kirikou using four Weapons at once.
One Piece has these in spades! On the Marines' side, it's usually Smoker and Tashigi or Hina with Django and Fullbody but most notably Coby and Helmeppo.** The Impel Down/Whitebeard War sagas gave us the Newkamas, several of which appear as distinctive background characters, such as a guy dressed as a reindeer and another wearing a bunny cowl.
Played straight with Yosaku and Johnny also probably the earliest example of this trope in the series. They're two of Zoro's old bounty hunting friends, and the most they accomplish is by lending Zoro their swords for his fight with Hatchan.
Ironically, Johnny and Yosaku are actually fairly important during the start of both arcs they appear in, where they each get their turn to be Mr. Exposition (Johnny in the Baratie arc and Yosaku in the Arlong arc), but when the action begins, they get demoted to this trope, especially when they get defeated off-screen by the Arlong Pirates.
Mahoromatic has Kawahara and Hamadi who, in the first season, exist mostly to procure and share porn with Suguru. In the second season, Hamadi goes beyond simple Two-Guys-hood when he develops a crush on Minawa. Kawahara still mostly stays in the background. In the manga epilogue, Hamadi is shown to have married Minawa while Kawahara is with Miyuki.
The two unnamed guys from Tokyo in Initial D who drive a Nissan Silvia S15. The fat guy who drives the car uses a technique called "SUPER ULTRA LATE BRAKING!!!" which only ends up screwing over his chance of victory.
Furihata, Kawahara, and Fukuda from Kuroko No Basuke, the three Seirin freshman who are almost always seen together, and rarely do much besides cheer for the team from the sidelines.
Kirby: Right Back at Ya! has a few of these. The most notables ones are Tiff and Tuff as well as King Dedede and Escargoon. There's also Meta Knight's assistants Sword Knight and Blade Knight. Not to mention Sir Ebrum and Lady Like.
Suzuki and Saito, Mashiro's two friends, in Bakuman。. They fade remarkably quickly even for this trope, and only show up again at a reunion.
Usokawa and Ketsukuma from Gakuen Babysitters, who are two male classmates of Ryuuichi and Kamitani that are seen the most and basically serve as as commentary for the other, more mundane aspects of the two boys lives outside of the babysitting club and their statuses as Chick Magnets, the latter in which every male in the class jealously chimes in on.
Tonpai Toda and Chinkichi Chida from Kochikame, who are two childhood friends of Ryotsu Kankichi that often join the young Ryotsu on his adventures. They mostly appear only in Ryotsu's childhood flashbacks, but do show up occasionly in the present day for a few episodes. One notable example being the three of them visiting their old school before its demolition and meeting with a girl who strongly resembles their now deceased childhood classmate who is revealed to be said classmate's daughter.