Cold-hearted assassin Kieth Baker and inept robber Sam Perkins in the Western manga Miriam. While they lack the duo dynamic usually present, and they don't usually work together, they fit the mold in a lot of other ways (like the customary occasional personality clash).
In the Cowboy Bebop episode "Boogie Woogie Feng Shui", Jet is pursued by two of these guys, who also appear to be based on the Blues Brothers.
There was also Ikazuchimaru and Kourimaru in Yu-Gi-Oh! GX (named Thunder and Frost in the dub), but despite having actual Elemental Powers, they were at most, Lumis and Umbra wanna-bes. The same can be said for Rikuo and Kaio in Zexal (named Scorch and Chills in the dub) who were possibly even worse. (Not only did they cheat against Yuma and Shark, it was rather obvious that they did so.)
Thorgrimm and Atli in Vinland Saga, up until Thorgrimm tries to make a play for power. Doesn't work out very well for Thorgrimm.
Hidan and Kakuzu. They both bicker a lot, and don't appear to really get along, but are partners nonetheless. Kakuzu being the smart one that comes up with strategy, and Hidan being the rash and loud-mouthed jerk.
Kakuzu:(having just reattached Hidan's head to his neck) Watch the stitches, they'll break if you move too much. Hidan: You know what, Kakuzu? Eat a dick.
The same is true for Itachi and Kisame and Sasori and Deidara. And then, after Sasori is killed, Deidara and Tobi.
Kinkaku and Ginkaku, the Gold and Silver Brothers, seem to fit. They seem inseparable. The weapons they wield requires they work perfectly as a team. And while sharing similar beliefs, their demeanor seem to be opposite. Kinkaku is more stoic and straight-faced. Ginkaku tends to smirk more. Kinkaku isn't very talkative, Ginkaku is the more loud-mouthed of the two. Kinkaku is taller, and more buff. Ginkaku is shorter, with a lean build. Kinkaku seems to be the smarter of the two, being he notices more things which he relays to his brother. Kinkaku also seems to be the stronger of the two, with Ginkaku calling for his help when he's in trouble. Two subversions happen here. Once Ginkaku has been taken down, Kinkaku's demeanor changes and he becomes more loud and wild. The anime subverts Kinkaku's expressions as well. In the anime, all of his manga frowns are replaced with him smirking.
Zetsu and... Zetsu. The left and right sides of his body have split consciousnesses and the halves communicate with each other via speech rather than thought.
Luke and Jan, the Valentine Brothers from Hellsing.
In the Zanpakuto filler arc from Bleach, the role is filled by the spirits of Rangiku and Momo's weapons, Haineko and Tobiume.
You wouldn't know it from looking at them (or listening to them), at least at first, but Walker and Erika of Durarara!! are absolutely terrifying. This is mostly because their dialogue primarily consists of anime and manga references, which would lead most people to think they're just kind of odd. Even better, their nerdy hobbies end up influencing their other hobby, so there ends up being quite a bit of dissonance between their relatively innocent love of anime and manga and their horrific threats.
Erika: We'll torture you based on the plot to one of these mangas!
The two thugs who actually pull off kidnapping Nagi, until Hayate's interference, in the beginning of Hayate the Combat Butler, show up later and kidnap Saki from Wataru's video store, until Sonia's interference, have this kind of dynamic between them.
Shiki gives us two young male vampires named Takatoshi and Yasuyuki, who are commonly seen together. They have two major scenes together, one in which they hunt down a villager, and another where they engage in conversation as they bury the corpses of those who haven't risen up.
Bunbee and Scorp would become a duo if Scorp didn't die so early in this season.
DokiDoki! Precure has the Selfish Deputies Leva and Gula who replace the Selfish Trio. Leva is the skinny guy with the brains, and Gula is the fat guy with the brawns. They are introduced together, summon Jikochuus together, fuse together and are killed together by Bel (the leader of the said trio).
Hansel and Gretel from the Black Lagoon animé. They even converse in a similar manner shown on the trope page.
In Brave10, there's Ichimaru and Niko, fairly ineffective ninja villains and comic relief who first appeared attempting to rape Anastasia during her introduction. They get their own omake segments at the end of every volume called "Ichimaru and Niko's Daily Grind" where they often end up complaining when they haven't appeared in the rest of the volume. They are absent from the anime adaptation, however, except for a brief cameo in episode five.