Megatokyo has Largo and Piro, Red Oni and Blue Oni respectively. Erika is also the Red Oni to Kimiko's Blue Oni, though they occasionally switch places.
Sluggy Freelance has Oasis and Kusari, two gymnastic assassins of mysterious origin with superhuman and probably supernatural powers. Oasis is basically insane as a result of Mind Control gone bad, which involved manipulating her emotional states. She is left impulsive and compulsive about the emotional reactions she was ordered to have before her controller was killed and is often incapable of rational thought. Recently, it's even be discovered that she is pyrokinetic, just adding to her fiery repertoire. Kusari obeys orders unfailingly, possibly also mind-controlled, but is still capable of rational thought and always remains cool. The two look about as identical as they can under their respective outfits considering that Kusari is always masked, but Oasis's most noticeable feature is her fiery red hair, whereas Kusari is always shown in the same bluish-purple outfit. There is speculation that the contrast between the two hides symbolism hinting at their as yet unknown origins.
The Continentals: A steampunk murder, mystery, sci-fi, adventure webcomic set in post Jack the Ripper England where Continental Operative Jeffrey Tiffen Smythe is the sophisticated, elegant, intellectual gentleman and his gender bending partner, the adventress Lady Fiona Fiziwigg, is a hot tempered, foul mouthed, do and say as I damned well please malcontnent and proud of it. It's a pairing of mismatched personalities that works surprisingly well as the two investigate a series of brutal "mangling" murders, uncovering a tangled web of intrigue, adventure--and murder!!! Find it here.
El Goonish Shive has Tedd and Susan, sort of. In this case, it's more of a personality difference as Tedd is generally upbeat and unobservant while Susan is a Deadpan Snarker. Other characters lean towards both sides, but generally hover in the middle.
Hanna and Zombie from Hanna Is Not a Boy's Name are a good example: calm, stoic Zombie (Blue) and impulsive, extroverted Hanna (Red).
Also works with a Hot-Blooded, uninhibited Casimiro and disciplined, well-mannered Finas. Even their color schemes are red and blue respectively.
There's also Doc Worth's Jerkass red to Lamont's nice guy blue. Although it's been shown that if anybody can get Lamont to lose his cool, it's Worth.
Karkat Vantas (red) and Jack Noir (blue) also have traces of this during their team-up in Act V, minus color correlations[1]. Karkat is impulsive, loud, and almost always angry at something, while Jack is cool, quiet, and moves with a chilling economy of effort.
Karkat, again, plays Red Oni to John's Blue once they start interacting. Their colour correlations match up as well, and Karkat's first conversation (from his perspective) with John is a textbook example - Karkat is a raging, capslocking, furious, hateful mess, while John responds with a cheerily oblivious "hi karkat!".
Also, cheerful, perky Jade (Red) to grim, dour Rose (Blue). Rose ends up playing Blue Oni to a lot of people, really; she's just about as blue as it is humanly possible to be.
Equius Zahhak, a stoic traditionalist, plays Blue Oni to the Red Oni antics of Nepeta Leijon, a genki roleplayer.
Juathuur. Dejoru is dark-haired, calm, and compassionate, with the talent to become a healer. Ratheel is loud, fun-loving, has red hair, and fights by making stuff explode. Partly subverted as Dejoru is capable of releasing an enormous amount of raw energy. Ratheel, on the other hand, is completely useless in each and every fight we see.
The Lawyers: Phil's red to Mr. Jones' blue. There is something of an inverted lampshade hung on this; Phil wears a blue tie and Mr. Jones wears a red tie.
Miko also plays the red to both Roy and Hinjo's blue
Ozy and Millie: Ozy blue (well, grey furred) and Millie red. Helpful that both are foxes.
In Girl Genius, we have the upbeat, charismatic Gil and the dour, calculating Tarvek. An interesting example in that they're both Sparks, and both schemers by admission.
Gunnerkrigg Court has an interesting example, where we were introduced to a red-haired Emotionless Girl (Annie) who befriends an impulsive gung-ho girl (Kat). Mutual Character Development, however, has by now reversed the roles almost completely.
Arguably, Sabrina and Zig Zag from Sabrina Online, the former being a somewhat reserved computer/Transformers nut and the latter an outgoing porn star legend.
Elf Blood has the KO Twins: SKO is the Blue Oni, being an adherent of law, order, and obedience, whereas TKO is the Red Oni, being the runaway renegade with a passion for freedom. Judging from a photograph taken when they were in school, however, this dichotomy may have been inverted in the past.
In Two Guys and Guy, Guy (and occasionally Wayne as well) is the red to Frank's blue.
The Wing Antivirus corporation from Electric Wonderland has modest (blue) Nathaniel Wing as software developer and his meglomaniac (red) wife Nina as CEO.
Kaustos and Two, Heiwa and Nandin, and others from Universal Compass. Almost every character has a foil because they are based off of emotions.
In Next Town Over, John Henry Hunter is a pyrokinetic outlaw with a suave demeanor and a zest for life, while Vane Black is a stoic, melancholic woman who eschews all pleasure and relations in her quest to kill Hunter.
4Komatose stars Ariake Shikima and Kyushu Miyamoto. Their hair, clothing and even speech balloon borders are red and blue, respectively.
9-year-old Phoebe and her unicorn friend Marigold in Heavenly Nostrils. Energetic Phoebe is red; proud Marigold is blue.
↑because trolls think fashion is stupid and Jack Noir is big on black