The eponymous hero started his adventures alone, but was soon joined by Captain Haddock. It's debatable whether the two are heterosexual or asexual, though they're both definitely Celibate Heroes. This is probably due to Herge not believing in including any romance in his works.
The detective duo Thomson and Thompson (Dupont and Dupond in the original French) probably count; though they look like twins, we're never given any indication that they're actually related.
Blake and Mortimer: together they fight pseudo-scientific crime... and sometimes sleep at each other's place from time to time.
The Bluecoats: In this American Civil War-set adventure comic, patriotic and often naive Chesterfield tends to consider Corporal Blutch to be a defeatist coward while cynical and pragmatic Blutch considers Sergeant Chesterfield to be an obnoxious blowhard, but they are virtually inseparable from each other.
Spirou & Fantasio, in which the two eponymous intrepid reporters live together in some incarnations of the series. Recently, one of the (many) writers went out of his way to mention that Fantasio was obviously gay and pining for Spirou. This is a rare case of Depending on the Writer in Franco-Belgian comics, as Fantasio has been shown to be very interested in girls in the earliest books, with usually horrible luck (except when using a Mind-Control Device to get kisses). Latest books have downplayed this, though. Conversely, Spirou, usually close to Asexual, has occasionally shown an interest in girls.
Asterix: Asterix and Obelix show some interest in women, but it seems like they still prefer to stay single and have more adventures together. They were even born at the same time on the same day according to the short story "Asterix's birth", which the druid Getafix proclaimed to be a sign that they would be best friends forever.
If you get away from the older/younger dynamic, "Tif & Tondu", "Quick and Flupke", "Johan & Peewit" (and this last case may actually also belong to the older/younger dynamic: Johan is clearly a young squire, but Peewit's age remains deliberately ambiguous, thanks to him being a little person; he may be as young as Johan or much older)...
Even, if you stretch it a little, Lucky Luke (with Jolly Jumper).
James "Biggles" Bigglesworth and Ginger Hebblethwaite in the Biggles comics. The BBC sitcom The Thin Blue Line makes a case that Ho Yay is in the air, but Inspector Fowler, who is a fan of the books, vehemently denies it.
Snoopy and Woodstock are the true epitome of a Peanuts example.
Calvin and Hobbes. The fact that one is aged six and the other is an imaginary tiger certainly helps.
Rudi and Freddy (German comic). Goes so far that they don't get an apartment because the landlady thinks they're really a gay couple, which she can't stand.
The eponymous duo of Quantum and Woody. Enforced by the quantum bands they wear; if they fail to knock their bands together every 24 hours, they turn into energy and dissipate.
Archie Comics has Archie Andrews and "Jughead" Jones. When people try to get one of them to stop associating with the other, they always refuse, regardless of whether it is Veronica, the teachers, or anyone else doing the asking. Of course, fans have often questioned the heterosexual part of it, but nothing in the comics has ever confirmed it.
Everyone's favorite non-affiliated coppers, Sam and Max: Freelance Police, have something like this, more like a Batman-Robin type deal but with more...uh...affection(?) by Sam to Max, and with significantly more insanity on Max's part.
Bone: Fone Bone, Phony Bone, and Smiley Bone are all three orphan cousins who have each other's backs. Part of their backstory is that Phony Bone had been a Parental Substitute to Fone and Smiley, and as the story progresses, Phony has to learn how to treat the other two now as equals and Heterosexual Life-Partners (and occasionally Band of Brothers).
The two incompetent rat creatures, Smelly and Stinky also qualify due to the fact that they are often seen together and address each other as "comrade". Their bickering is mostly similar to that of an old married couple.
Surprisingly for a Porn with Plot series about sex-positive women, all of the women in Kevin J. Taylor's Girl series fit this trope rather than the expected girl-on-girl action, specifically between main character Jaliera Dane and Jessie James, and to a lesser extent, Jill with either woman. They've shared the same men, casually slept naked together in the same bed even without men and showered together, but not even a flirtatious word to each other. Jessie even lampshades how one of the guys expected took pictures with her camera hoping to catch this just because she and Jill were showering together when there wasn't even any "skinship" going on.
Jessie: Those pricks came into our bathroom and shot us in the shower. I guess they were expecting some kind of lesbian shit. Assholes.
Mandrake the Magician and Prince Lothar have been partners in stage magic and Bash Brothers fighting the forces of evil for years and years.
of this obscure Golden Age feature, Jill and her gal pal Daisy are almost always together. And no sign of boyfriends for either of them....