A Crown of Stars: Shinji and Asuka. Their numerous battles together in the past are mentioned. Moreover, Asuka's new Humongous Mecha is a two-seater, allowing Shinji and Asuka sitting together in the cockpit.
He smiled at her in the comm window. "You said it, Asuka. You finally said it." She blinked at him. "Said what?" "'I love you.'" Asuka stared blankly at him for a second before it sank in. Her eyes widened. "Well scheiße " she said eventually. "So much for talking about it tonight in more romantic surroundings. When I said 'right before a battle isn't exactly how or where I want to talk about this', I did mean it." Shinji's smile got bigger. "Somehow, right before a battle for our lives seems fitting for us."
Advice and Trust: Shinji and Asuka, natch. And given the nature of Evas, they're not merely more competent as a result, but more powerful as well.
The Child of Love: It took a good while for them to open up to each other, but Shinji and Asuka got together and kept fighting giant monsters together. In chapter 3 it is not until Asuka rushes in the battlefield that the team gains the upper hand. In chapter 7 she does not fight directly due to her pregnancy, but she provides tactical support. After giving birth she and Shinji fight in tandem.
Sif and Loki, after the finally get together at the end of the first book, though they don't always fight side by side, given that she's the Goddess of War (especially close-quarters-combat) and Loki's skills tend more towards skulduggery and command-and-control level sorcery.
Uhtred and Jean-Paul become this once they get together, despite Jean-Paul's distaste for fighting - all it means is that he prefers not to fight, and that when it comes to it, he will end the fight quickly. Which, in an imaginative and exceptionally powerful speedster with more pragmatism than scruples can get messy.
Shinji and Asuka (reinforced since their engagement). Misato even commented that both are hyper-aggressive.
Kaworu and Saburo when they were dating.
FuzzyMemories has Tempest and Zetsu, who have a strong and healthy relationship, but nonetheless are both badasses in their own right, and by the special of the series, the two are now on-par enough that the latter can actually keep up with girlfriend in terms of hunting and fighting, despite not being nearly as close to her strength.
Ghosts of Evangelion: Shinji and Asuka are one during the War. Thirty years after the conflict their experience fighting together still helps them beat games together.
HERZ: Shinji and Asuka, although due to Unit 02 getting repaired they are not seen battling in tandem until the Final Battle when they sortie together to fight the SEELE forces.
Higher Learning: As their relationship strengthens throughout the story, Shinji and Asuka become an efficient fighting duo.
Legacy: Thea and Roy become one of these in this Arrow sequel. When they suited up as the Arrow and Canary 2.0, witnesses said watching them fight was "like watching the principal dancers of the Moscow ballet.
Once More with Feeling: Asuka and Shinji started on the path to becoming one as of battling the Sixth and Seventh Angel. They fought together and performed spectacularly.
Not that Shinji could begrudge Asuka her grand entrance. Perhaps she hadn't exactly covered herself in glory today but by the same token; he couldn't have done it without her. Not for the first time, he smiled slightly at that thought, working side by side with her again; Asuka the burning sword, Asuka the raging, unquenchable firestorm-
The One I Love Is...: Shinji and Asuka. Due to living, working and fighting together, they started to like each other and became extremely close. This closeness kicks the plot off when Rei realizes Shinji is falling for Asuka and decides to pursue him actively.
Purple Days: Joffrey and Sansa become one after Sansa is brought into the "Groundhog Day" Loop and starts training in martial arts and magic. While Sansa will never be Joffrey's equal in combat, she's grown skilled enough to hold her own on the battlefield and has her newly developed mastery of shadowbinding and other dark magics to make her just as deadly as him.
Scar Tissue: Shinji and Asuka. During the Angel War they battled giant alien monsters together despite of their fights and arguments. In chapter 17 Asuka's Humongous Mecha is modified so that Shinji and she can pilot in tandem and fight together. Shinji also tells her he will not leave her to fight alone again.
The Second Try: Shinji and Asuka, even more than in the original series now that they are serious about fighting, have gotten over their crippling psychological and emotional problems, and want to support and help each other. It even is noted by Kaworu.
In the second-to-last episode:
Asuka (to Shinji): I'll handle them. These guys aren't the real problem after all. Just take care of my cable, okay? Shinji (smiling weakly and nodding): Of course.
And later in the same episode:
General: Concentrate all fire on that power cable! Comm-Officer: It's no use, Sir! Purple's guarding it!
Robyn Wilde and Hannah Savage from Take a Stand: Star of Ceartais, who begin dating a while after the start of the story, become this once being recruited into Team Ceartais as (respectively) the Undying Scarlet and Bullet.
Thousand Shinji: Shinji and Asuka began to strongly bond when Shinji told Asuka that they should fight together to destroy their enemies. From that point they became partners-in-battle and shortly after they got together. The results were bloody for their enemies.
Some Semblance of Meaning: Near the end of the 44th Hunger Games, Vale and Obsidian become one of these. Although the latter doesn't want the former to be put in harm's way, she does manage to save his life at least once.
Crossover Chaos has quite a few examples. Killer and Beetle become this after they get paired up in v1, as well as Kyle and Lindsay once they join C.H.A.O.S early in Agents of C.H.A.O.S.
Khan and his lover, Victoria, are this in the Star Trek (2009) fanfic Safe and Sound. During the Eugenics Wars they apparently marched into the Taj Mahal, and after the ensuing battle (during which Victoria killed thirty armed guards with her bare hands while saving Khan from them; it's not mentioned how many Khan killed) they marched back out again having claimed the building as theirs.
Life After Hayate explains that this is a family tradition with the Harlaowns, to the point you are not considered acceptable dating material unless you've partnered with your desired date in combat. It's not necessary to fight directly alongside them, but close dependency in a combat situation is absolutely non-negotiable: Amy Linetta was allowed to date Chrono because she had been his "angel on the shoulder" as Arthra's combat controller. Lindy and Clyde supposedly met on the bridge of a warship in action; Chrono's grandmother and grandfather met when their units were assigned to the same battle. Chrono expresses relief that Fate is interested in Nanoha because she already meets the standard.
Donald and Daisy combine this trope with Dance Battler in the jungle concert scene.
Cinderella and Prince Charming do this as well, teaming up to rescue the Disney Princes.
In chapter seven of Bait and Switch (STO) a pair of junior officers from the USS Bajor's security department, Lieutenant (JG) K'lak and Ensign Kate McMillan, go on an away mission with Eleya and act as a sniper and Target Spotter respectively. In the next chapter Eleya catches them meeting up in Ten Forward, and McMillan gives K'lak "a peck on the cheek that looks a lot more than just friendly." Eleya alludes to moving McMillan to a different supervisor.
Petra and Brynjolf in Drakonophobia though prone to splitting apart, there are times where they really work well together, before and after they actually get into a relationship. And The Nerevarine fights alongside Older!Ayisha often as well, as warrior and mage respectively.
In Discworld fic Whyand Were, Assassin Johanna Smith-Rhodes provides the muscle and fighting ability; wizard Ponder Stibbons is the magical half of the relationship. It is established over several stories, especially in Slipping Between Worlds, that she would kill for him and he would put his life on the line for her.
Kim and Shego in the Kim Possible fanfic At the Centerfold of the Storm. Unlike in most Kigo fics that focus on the two settling down and starting a family, Kim and Shego decide to continue in the Secret Agent/Super Hero line of work, such as battling volcanoes, fighting Humongous Mecha on foot and taking on the entire criminal underworld.
Although they're very much one in canon already, it shows with Han and Leia in the Star Wars fic The Princess And The Pirate. Han, Leia and Luke have ended up captured. Han's already been dragged off and severely beaten once. He's got assorted fractures, bruises, internal injuries and a high fever. But the moment some of the guards start turning their attention to Leia, Han's on his feet, giving them a Death Glare and warning them that they're dead if they touch her. They do realize that he means business, even in his condition. Later, when they try dragging Han off again, Leia unleashes on them with Force power, because there's no way she's going to let her husband get tortured some more.
In the Infinite Stratos fanfic, Infinite Stratos: To the Other End of the World, there are quite some battle couples. Hackers are trained as Bash Brothers, but in later chapters, the hackers discover they can work pretty well with Infinite Stratos pilots as well. An example that is most prominent are Kerlongsj and Chifuyu fight as one and they take out an entire army with just the two of them. Due to their history, they're quite good at it, despite the huge difference in style, weapons and special powers.
In AAML: Diamond and Pearl Version, Ash and Misty swiftly become this after Misty rejoins Ash during his travels in Sinnoh, with the two developing a comfortable routine working together in double battles; their common team-ups either call on Charizard and Gyarados when facing opponents they need to overwhelm with raw power or Grotle and Vaporeon when they need a less direct approach, the first two being their powerhouses while Grotle and Vaporeon represent Force and Finesse.
In the Stargate SG-1 series What You Already Know, Daniel Jackson and Sam Carter have no problem fighting alongside each other as their relationship unfolds, with Daniel's psychic powers mixing well with Sam's military experience, although they have to be granted special dispensation to continue their relationship after Sam is promoted to team leader.
Asuka and Shinji in Neon Genesis Evangelion: Genocide are a couple and when they're together, they fight better and harder. When Samael fought both, it defeated Asuka, but when it was about to crush Shinji, Asuka went berserker and killed Samael. They also fought the MP-Evas and the final Humanoid Abomination back-to-back.
Blood and Honor: Sanguis and Quinn, though they go back and forth on the "couple" part for about half the story due to Quinn's personal issues. Eventually they end up together on and off the battlefield. Sanguis typically gets in close with her lightsabers to take out the biggest threat while Quinn uses his brains and blaster to wreak havoc from a distance.
Both of the main couples in the Twice Upon an Age series do this a couple of times; given that it covers the events of Dragon Age: Inquisition, it's par for the course. Mahanon and Cassandra get more opportunities, because Cassandra is an active party member, but Cullen and Victoria take a few turns when circumstances permit it. Dorian and the Iron Bull also fall into this occasionally, and it's indicated that so do Varric and Bethany at least once.
Varric and Bethany gradually evolve into one of these in Beyond Heroes: Of Sunshine and Red Lyrium. It becomes obvious enough that the companions start remarking on it.
Most couples in Son of the Sannin are shown fighting side by side at one point or another (Naruto and Hinata being the most prominent example), but special mention goes to Shizune and Shisui, who team up with the intent to kill Danzo after he has their infant children kidnapped.
Spotless: When Master Fu finds out that Kagami knows Marinette's secret identity, he meets her in person and decides to give her the Dragon Miraculous full-time.
Frail Equilibrium: Dante and Tess gradually develop the rapport to fight as a duo - complete with their own little inside jokes. As some unfortunate demons found out, the only thing worse than fighting Dante or Tess is fighting both of them.
In Tales of the Otherverse, super-heroines Supergirl (Kryptonian) and Rogue (power-leeching Flying Brick) get together and found their own super-hero team.