Considering the number of Robins Bruce has gone through, the "life partner" part doesn't totally apply. A more straight example would be Batman and James Gordon, going as far back as Gordon being the first one to console Bruce after his parents' death, and Year One where they were basically the first true ally they had in their struggle to clean up Gotham. Gordon is one of very few people outside the Bat Family or the Justice League that Batman will trust with his life.
Robin/Red Robin (Tim Drake) and Superboy (Conner Kent)
Conner: As far as I'm concerned, you're my Robin. Always will be.
Tim: And you'll always be my clone boy.
After Conner's death, Tim changes his Robin costume from the traditional red and green to the more somber red in black, explicitly in honor of Conner's colors.
Tim spends a great deal of time trying to clone Conner after his death. He almost allies himself with Ra's al Ghul at one point in order to perfect his cloning technique.
The last thing Tim thinks of when he almost dies after being attacked by the Council of Spiders is how he'll get to see Conner again.
Robin, Superboy, and Bart Allen/Impulse/Kid Flash 2/Flash 4. For a lot of people, the three of them are a One True Threesome.
Cable and Deadpool in, well, Cable & Deadpool (although many fans perceive this as going straight into Ho Yay). They are extremely close despite Deadpool's personality being obnoxious even at the best of times, and Deadpool was the first person Cable pictured/made psychic contact with while trying to decide whether to blow himself up. They were genetically commingled, so that "one phone call" would have happened even without intent....And Cable needed to make that contact to manipulate Deadpool into Doing The Right Thing.
Deadpool is an omnisexual due to his mental instability, but there is not enough evidence to prove anything more than this trope.
Deadpool and Weasel could also fall under this trope.
Both C and D are well aware of their Life Partner status, especially evidenced when they both regularly called the time during a small falling out between them ("Small falling out" in this case being Deadpool's new membership in a mercenary group hired to destabilize Cable's fictional country Providence. Said membership was revealed when 'Pool shot Cable in the back of the head.) a "divorce".
Hell, once when asked about his relationship with Cable by well known gun-for-hire The Cat, Deadpool responded that it was a 'Don't ask/Don't tell deal'. Feel free to interpret that however you wish.
The Cat:...don't ask don't tell? Oh...OH!
Luke Cage and Danny Rand, also of Marvel Comics, with Luke going so far as to name his daughter after Danny.
Their close friends Misty Knight and Colleen Wing also are considered Heterosexual Life Partners, with Luke Cage going so far as to recommend the two get "gay married."
When Danny is asking Luke to join his new non-profit, he says 'I love you with every fiber of my being'.
Booster Gold and the Blue Beetle (hereafter "Boostle") of JLI fame are probably the most prominent Heterosexual Life-Partners in The DCU. One storyline in Booster's comic involves Booster time-travelling to keep Beetle from being killed; when he is told this has the potential to destabilize the entire multiverse, he decides Beetle is worth the risk.
When encountering former (dead) Flash Barry Allen while cruising through the time stream, this exchange occurs:
Beetle You 'rear-ended' Barry Allen?
Booster Oh grow up!
There's also the scene where, after one of their "break-ups", Booster trails Ted in a public place and begs Ted to take him back.
Beetle Get a grip, Booster. You're acting like some jilted lover.
Booster Well, that's what it FEELS like!
Beatriz "Fire" DaCosta and Tora "Ice" Olafsdotter. It was even in-canon -mistaken- for gay when Tora was temporarily dead and her replacement, who (for some reason) looked a lot like her, misunderstand Bea's mourning. Admittedly, Bea was really off the deep end but still. The way it was written it did seem to indicate that Bea's close friendship towards Tora had sapphic undertones and that the resultant subconscious sexual jealousy was a big reason for Bea's sometimes extreme antipathy towards Tora's boyfriend, Guy Gardner. Once Icemaiden made her face up to that, Bea could learn to appreciate Guy's good qualities, and for a time the two found solace in each other's arms.
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 being a devout (liberal in later years) Catholic who didn't believe 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.
In the American Civil War-set adventure comic The Bluecoats, 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.
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 interest to girls.
Astérix came a few decades after the previous examples, with Asterix and Obelix.
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).
And Oliver Queen and Hal Jordan - one Waid story had Barry jealous of the time Hal spent with Ollie.
Hard Traveling Heroes was full of this. And it was lampshaded by Kevin Smith in his early run by Roy Harper (Red Arrow/Arsenal), saying that it was "typical Ollie, get a kid ward, train them, get close to Dinah then leave them both to go hang out with Hal". This is AFTER Queen had come back from the dead, and was brought to the afterlife to talk with Hal Jordan/Spectre to see what was up.
Previously, villains Black Tom Cassidy and the Juggernaut.
Also Previously, Wolverine and Nightcrawler.
Also Nightcrawler and Colossus. Sometimes two would fight over the other like jealous girlfriends. Nightcrawler and Captain Britain too, though they didn't always get along.
Magneto and Professor X: a tragic case of a broken life partnership, and Depending on the Writer Magneto especially regrets that their ideologies have driven them apart.
In a similar, though more jarring sense, Cyclops and Wolverine, with their recent breakup and both sliding down different slopes. Prior to this, the two were often at each other's throats but in a manner similar to two brothers, and when push came to shove they'd be as thick as thieves. In fact, once Jean Grey (Scott's long time love and late wife, and the woman Wolverine had the hots for) died, thus removing the main source of their bickering, the two notably stopped arguing so much and became more openly close and friendly. Then Wolverine became a hypocrite and Cyclops became an extremist, and now the two can't stand each other.
Teen Titans: Beast Boy and Cyborg. Cyborg is often bitter at what he frequently sees as the loss of part of his humanity, but Beast Boy can always cheer him up. Conversely, when Beast Boy hits a few too many points on the dingbat meter, Cyborg can bring him down to earth.
Depending on the writer, Dick Grayson (Robin I/Nightwing/Batman III) had this with either Wally West (Kid Flash/Flash III) or Roy Harper (Speedy/Red Arrow/Arsenal). Or both.
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.
Tony and Steve are almost in a bizarre, giant ass HLP Dodecahedron, given how many people they share this relationship with. As well as each other and the mentioned above, Tony, Depending on the Writer, has a, slightly more vitriolic, one with both Bruce Banner (one played up in the recent Avengers film) and Henry Pym, while Cap also has one with Clint Barton. Clint Barton, meanwhile, has one with Henry Pym too, making things all the more circular, while recent developments have given Hawkeye something similar with Captain Britain. Captain Britain, meanwhile, held a similar, though more aggressive, relationship with Nightcrawler, and, inspite of introductions, a more pleasant one with Pete Wisdom.
One of the major changes from Pre Crisis to Post-Crisis is the removal of this trope from Batman and Superman's relationship. The impact of Batman: The Dark Knight Returns, as well as Character Development in the Bronze Age that had turned Batman back to his dark roots, set the stage for relatively little kerfuffle over the retcon, the reasoning being that their "true" personalities (friendly, laid-back reporter versus gruff, brooding vigilante) were too different to get along.
And now it's back to Heterosexual Life Partners status, with the launch of the Superman/Batmantitle.
In the New 52, they went from "distrustful, yet respecting" of the other, to actually pretty good friends. A new book, Batman/Superman, even details how they first met and shared adventures for the duo. Batman even keeps Superman & Wonder Woman's relationship a secret for as long as he could out of respect.
Rocket Raccoon and Groot. As the series went on, Rocket's relationship with Groot went from wanting The Big Guy for back up to this. And it only became more apparent after the Timely Inc. mini-series as they're currently the only active members of the Guardians of the Galaxy.
X-23 and Jubilee, the two 'daughters' of Wolverine who have similar issues. It's a tad darker than normal as it partially formed out of the two each agreeing to take the other down if they lose control.
Jessica 'Spider-Woman' Drew and Carol 'Ms. Marvel' Danvers (now Captain Marvel). They're even approached as a pair during the recruitment drive in Avengers #2, while everyone else, except for Cannonball and Sunspot (another pair of Life Partners), got approached individually. Carol also has one with the other Jess, Jessica Jones; not surprising, given that Jones was an expy of Drew when first created.