Pete White and Master Billy Quizboy from The Venture Bros., who are also business partners and roommates in addition to being super-scientists. In fact, most of the series' characters are foils for one another; Doctor Venture and Brock, The Monarch and Dr. Girlfriend, Hank and Dean, Watch and Ward, Monarch Henchmen 21 and 24, etc. In DVD commentaries, Doc Hammer and Jackson Publick point this trope out and confess that this is because whenever they're stuck or bored while writing they just make up two characters who are basically each other and goof around doing voices as them.
Several such pairs exist in Transformers Animated: Blitzwing and Lugnut, Bumblebee and Bulkhead, and Mixmaster and Scrapper, and Snarl and Swoop. In the Transformers comics, Rack'n'Ruin of the Wreckers, who were bonded together in a desperate attempt to save their lives. The fact that they basically have one name (and it's never specified which is which), and that they receive basically zero characterization even as a pair makes them a perfect example.
Brian and Stewie have played this role in episodes where they are the focus.
Cleveland and Quagmire fit Those Two Guys until Quagmire started getting his own episodes and Cleveland got his own show.
Tomik and Belgarde, the two blond guys from an unspecified region of Europe "who have been living in the United States almost long enough to sound American." It's is not clear who is Tomik and who is Belgarde, and it probably doesn't make a big difference.
Baljeet and Buford have become this quite quickly, with an interesting Friendly Enemy dynamic as well.
Major Monogram and Carl.
Sometimes, in episodes that focus on Candace, Perry or Doofenshmirtz, Phineas & Ferb themselves get demoted to this.
Two guys that remain minor from beginning to end on the show are the nameless husband and wife. They're in several episodes for the sole purpose of the same Running Gag. The wife will say, "I can't believe you bought a [fill-in-the-blank product] [fill-in-the-blank product rental/selling place] that didn't have any [fill-in-the-blank products]. What, did you think [fill-in-the-blank products] would just fall from the sky?" Then, the [fill-in-the-blank product] will indeed fall from the sky, usually landing on top of the wife.
Joey, Jeffy, and Jamie from Daria. They pretty much exist just to remind us that Quinn is attractive when she doesn't have a Boy Of The Week around to do it instead. In fact, they're SO Those Two Guys, Jamie is usually called something else, only to fruitlessly repeat that his name is Jamie.
It introduces Snips and Snails, a pair of excitable boy unicorns, in the episode "Boast Busters".
Lyra and Bon Bon were put side-by-side in the background often since their color-schemes complimented each other. The fans noticed and they became this thanks to a combination of Ascended Fanon and Ho Yay.
Twilight Sparkle and Spike have this chemistry at times, usually in episodes where they are supporting characters.
The show also occasionally likes to pair certain ponies together for particular episodes, even if these examples aren't nearly as consistent due to spotlight rotation. Rainbow Dash seems to form a good few of them (usually with Applejack or Fluttershy).
In the Teen Titans episode "Things Change", the girl who may or may not be Terra is flanked by two unnamed schoolgirls who seem to be her friends.
In Astérix and the Vikings, Asterix and Obelix take this role, with Justforkix as the main character. This is particularly silly, since Asterix's name is in the title of the film, and Justforkix was only a (to be fair, strong and memorable) side character in Asterix and the Normans, the comic the movie is adapted from. One reviewer on That Guy with the Glasses complained it was extremely strange since Asterix and Obelix are better-written, better-animated and designed, and easily the most interesting and likeable characters in the film, yet are relegated to backup for a whiny brat who gets no comeuppance.
Youngmee, Sue, and Jasper in Littlest Pet Shop (2012). Of these three, Youngmee gets preferential treatment by the writers by virtue of being neighbors with Blythe, the protagonist. And Youngmee becomes the only other human to know Blythe's ability to talk to animals.
Vinnie and Sunil. Almost to the point of them being a couple.