In Angel Fred and Wes have a battle couple scene at the end of "Smile Time" and in the beginning of "A Hole In The World".
Fred and Gunn during Season 3 and 4 before breaking up.
Angel and Cordelia several times in Seasons 1-3, they even train together in the basement.
As seen in multiple flashbacks Angelus and Darla were a Battle Couple for 200+ years, cutting a bloody swath Europe and were soon joined by Spike and Drusilla in what is essentially the demonic version of ABBA.
Ollie had a brief fling in Season 1 with the Huntress in the hope to curb her more violent tendencies and in Season 2 hooks up with the original Canary after finding out who she is. Sara herself was implied to have been Nyssa's lover during her time in the League of Assassins and left because she got tired of the life of an assassin.
As part of the background, John Diggle and Lyla Michaels met during their time as soldiers in Afghanistan, then got divorced. After Diggle became part of Ollie's crusade and Lyla joined ARGUS, then reunited and even got remarried.
Delenn, while in command of four very nasty warships: Only one human captain has ever survived battle with a Minbari fleet. He is behind me. You are in front of me. If you value your lives, be somewhere else!!
Buffy and Angel, who spent a lot of time fighting evil together and were nearly unstoppable. He left after season 3, but they got to fight one last battle together in the series finale.
Buffy and Riley, until he lost his heightened abilities when he stopped taking The Initiative's drugs. Unfortunately this was one of the factors leading to their break-up, as Riley's lack of superpowers meant he couldn't keep up with Buffy in a fight. Riley returns for "As You Were" in Season 6 where he's married to a Badass NormalAction Girl, forming a new Battle Couple.
Burn Notice: Burned CIA-spy Michael and former-IRA member, gun runner, and explosive-experts Fiona are not to be trifled with, alone or together. Possibly best illustrated in the episode Better Halves, where Fiona and Michael take on the superior numbers of a Russian strike team with each other at their backs.
Rick Castle and Kate Becket from Castle: She's a New York PD Detective and he's a tag along writer. Together they fight crime! Kate will never admit they are a couple but Everyone Can See It so she doesn't have to. They have been together since the beginning of season 5.
Charmed: The woman, Piper, who is the more aggressive one, and the man, Leo, is the more peaceful one. When it comes to the safety of their children, the opposition tends to explode spectacularly.
Chuck and Sarah become this late in the third season. Especially evident in "Chuck vs. the Honeymooners", when their fighting (while cuffed together) looks a much like a dance as a fight, and in "Chuck vs. the First Fight", where they fight bad guys while quarreling with each other.
Sarah and Bryce were this before she and Chuck came across each other. In "Chuck vs. the Nemesis", Chuck's reaction to watching them fight together was a dazed, "Wow. They really are great."
Danny and Lindsay from CSI: NY both spend a lot of time fighting bad guys and there have been a lot of flying bullets in their romance.
Daredevil (2015): Matt Murdock's relationship with Elektra Natchios in season 2 is built around her having been sent by Stick to seduce Matt and bring him into Stick's war with the Hand. In season 3, Matt's romance with Karen Page hinges around their prior sexual tension and their team efforts to take down Wilson Fisk.
Dexter: Dexter and Lumen become this in Season 5. Instead of battle, they're both serial killers.
The Doctor and River Song; he is a Memetic Badass both in-universe and out, and she is a part-Time Lord genetically bred child created as a weapon to fight the Doctor. She fell in love with him instead. They've fought off alien invaders back-to-back, while flirting and their names strike fear in villains everywhere. River once made a Dalek beg for mercy! They're married!
In the serial "Battlefield", Ancelyn and Brigadier Bambera start out beating on each other and end up as a glorious example of this trope.
Madam Vastra and Jenny Flint; sword-wielding interspecies lesbian detectives who fight crime in Victorian London (and sometimes other eras). The 2012 Christmas special confirms that they're not just together, they're married.
Dollhouse: Paul and Echo successfully watch each others' backs through ten years and an apocalypse.
Farscape: John Crichton and Aeryn Sun. A slight variant, as he starts off being mostly useless in combat (he was a scientist before he was shot across the universe), but by the end he's not only protecting her as much as she protects him she finds his insane "plans" and constant, nigh-incomprehensible-to-aliens pop culture references charming and fun. Perhaps best shown at the start of the Peacekeeper Wars. They are reformed after two months Not Quite Dead in the same passionate kiss they were in before. They pull apart, stare tenderly into each others eyes, and at the exact same moment pull out their weapons and have the whole room covered. It's awesome.
Wash and Zoe have faced a great deal of danger together. Interestingly, Zoe is the warrior of the couple. Her husband Wash is an Ace Pilot. He might fool viewers at first, but he's pretty badass and shows off in "War Stories".
Zoe: Take the helm, sir? I need this man to tear all my clothes off. Wash: Work, work, work. . .
Downplayed in Zoe and Mal. Despite fighting through the war and facing life and death together, there is no romance between them, as we see in "War Stories". They are close and tight friends, but definitely not a romantic couple. When they tease her husband with a bit of awkward flirting at the end of the episode it's described as "downright unsettling".
Generation Kill: Subverted Trope. One of the Marines receives a letter from his My Girl Back Home. She announces that she has enlisted in the Marine Corps to be able to fight alongside him. He is annoyed by this because, not only is she ineligible to join Marine Recon with him, she could potentially be deployed somewhere away from his own duty station.
In Hannibal, Will and Hannibal officially become this in the final episode when they take down and kill Francis Dolarhyde, the Red Dragon. The looks they give each other can only be described as "fuck-me eyes".
Hart to Hart: Yet another battle/spy couple are Jonathan and Jennifer Hart.
Kamen Rider Dragon Knight: Features Len and Kase, who are separated for the first half of the show due to her being MIA from a previous battle that didn't go well. Unlike the general version of the trope, they're both superheroes that fight physically; "magic" is only used to boost the power of their normal attacks.
Lost: Kate and Sawyer used to a formidable tagteam regardless of their relationship status at the moment. Kate also occasionally had this with Sayid.
Miami Vice: Tubbs and his on-and-off girlfriend Valerie, an NYPD homicide detective played by Pam Grier, are this during the few times they're paired together.
Lamie and Grifforzer in the series' source material Kyoryu Sentai Zyuranger were an evil example as the two were married. This was only hinted at with their respective western equivalents Scorpina and Goldar(they were dating according to a cancelled episode).
Once Upon a Time: Prince Charming and Snow White; he's a badass with a broadsword and she's skilled in both archery and swordplay. When the Queen shows up at the wedding she unhesitatingly drew Charming's sword.
Emma and Hook have progressed from flirty enemies to allies to friends to this over the course of the show. Their typical response to the other being in danger is to get dangerous and kick the ass of the aggressor.
Once Upon a Time in Wonderland has Alice and her Genie lover, Cyrus. Training with swords doubled as flirtation for them, and they fought off numerous attempts to steal the bottle during their many adventures. In one flashback, the couple is ambushed by bandits, and Cyrus cheerfully informs them that Alice is the one they should worry about. He's right, of course, and the couple quickly drive their attackers off.
Robin Hood: From the BBC's show: not so much Robin and Marian (they are rarely seen fighting together), but outlaws Will Scarlett and Djaq. Their first act as an official couple is to kill a man, after which Will informs the corpse: "She's with me."
Sharpe: Richard Sharpe and Teresa Moreno from the novels and TV series are the archetype. They met fighting in Spain. They fell in love, married and had a daughter (not necessarily in that order). In between these episodes, they fought against Napoleon's armies in Spain.
Spartacus and Sura kick ass together in the first episodes, and when Spartacus dreams about her or thinks up his escape plans they are always fighting together.
Later Spartacus and Mira; Mira is not a gladiator but she's ferocious with a knife, and they fight together multiple times.
Crixus and Naevia count as well; at first was Damsel in Distress, but then Crixus taught her how to properly chop off heads, and now they happily slay Romans together.
Agron and Nasir fought together before they became a couple, and now that they are together they continue to kick Roman ass.
From the prequel we have Barca and Auctus, who trained and fought together for many years.
Stargate SG-1: Rya'c and Kar'yn become this in the episode "Sacrifices". This trope is lampshaded and used to justify their marriage when they face opposition from Teal'c on the basis that Rya'c has chosen to fight the Goa'uld and that war has to be his priority. As Ishta points out, "A warrior is always stronger with another at his side" so being a Battle Couple will be better for both them and their cause.
Odo and Kira provide the page quote, from toward the end of the series. Although Kira was typically more the combatant, Odo held his own in commando raids and intel.
All Klingon relationships. Klingons adore Battle Couples and they are Older Than Dirt in their culture. Not only is there the legendary pair Kahless and Lukara but stories of Battle Couples go back from the legendary to the mythic when the Klingon Adam And Eve decided to sack the heavens together instead of fighting each other. In every Klingon marriage an important part is promising to be a Battle Couple. Worf and Jadzia Dax tended to have their most dramatic moments exemplifying this trope.
Many Bajoran relationships fall along similar lines to the klingons.
Quark started a battle couple relationship in order to court a Klingon Noblewoman. This is the same episode where Jadzia and Worf first hook up (while playing matchmaker for Quark). The ending plays this for laughs as both couples end up in the infirmary due to injuries sustained during their Klingon-style lovemaking. Dr. Bashir subsequently swears off asking people "how did you injure yourself?" because he really doesn't want to know.
Jonathan and Nancy team up to try and kill the Demogorgan in Season 2, played with in Season Two where despite becoming an Official Couple they do more spying than fighting. Played wonderfully straight again in Season 3, where Jonathan and Nancy kill their infected boss Mr Holloway and Bruce their asshole college together at the hospital.
Hopper and Joyce enter the Upside down together to save Joyce's son Will, however despite being sweethearts in highschool Hopper and Joyce aren't a couple or at least won't admit to being so. Season 3 plays it mostly straight as Hopper and Joyce fully realize their feelings for each and save the day together, then Hopper seemly dies.
Villainous example with the Mind Flayer possessed Billy and Heather.
Ethan Chandler and Vanessa Ives of Penny Dreadful during the episode "And Hell Itself My Only Foe". When Pinkerton agent Warren Roper shows up to forcibly bring Ethan back to America, threatening also to rape and kill Vanessa, Ethan and Vanessa both end up attacking him, simultaneously kicking (Ethan) and stabbing him (Vanessa) to death.