This is the competent converse of the Red Shirt Army.
They are not the protagonists, but just their support (or cavalry). We probably won't get to know many of them well, though those we do meet we'll probably know better than a Mauve Shirt. As far as Character Focus goes, they could be Cannon Fodder...
...but they are notCannon Fodder. Most of them still have no names given and will dress alike, but unlike the Red Shirt Army, they will live. Furthermore, they are competent at fighting their enemies, especially those who can kill just by one looking at them funny; they are truly helpful in a tactical situation (or "hot zone"). Whether this help is acknowledged depends on the writer.
They can hit their opponent most of the time. Regardless of how many hits they take, they can go head-to-head with the enemy without being wiped out in seconds, and often without losing any men at all.
The key difference between these guys and a Badass Army is that they are not technically an army. Usually they'll be a relatively small and elite fighting force, and they're more likely to answer to a single individual or be devoted to a specific cause. Contrast with Badass Crew, which will also encompass a small team, but is made up of distinct characters and more likely to be the focus of any given story.
Named for Robin Hood's army of outlaws in the classic film The Adventures of Robin Hood (known as the "Merry Men" in folklore). Not to be confused with Brad Sherwood.
The GM in Mobile Suit Gundam is the mass-produced version of the Gundam. They're completely expendable, but they hand out as much punishment as they take. While the central protagonists are equipped with the Super Prototype, it's the GMs in the background who won the war. Such as the Londo Bell, an army of aces.
There is another memorable instance in Gundam Seed: in the final episode, Athrun and Cagalli are fighting their way through Jachin Due to try to get to Athrun's Archnemesis Dad Patrick. They are accompanied by a third mobile suit pilot who is fighting just as hard as they are with a submachinegun in one hand and throwing grenades with the other. This fellow does not have any dialogue and wears a polarized helmet so we don't even see his face, but what's notable is that he survives the entire assault (in this series, that's really saying something)! While Patrick dies in his son's arms, this nameless soldier stoically stands next to him watching the whole thing unfold, and he is also seen evacuating with Athrun and Cagalli when the fortress begins to self-destruct.
Anonymous Bureau Mages in Lyrical Nanoha series, they are good at doing their job as inter-dimensional magic police, and could hold of against hordes of enemy Mooks thrown at them, just not good enough to face the main villains that even the Protagonists find hard to handle with.
In Guilty Crown, the United Nations task force sent to stop the GHQ in the final two episodes. At first they seem like a Redshirt Army when a powerful Void Genome destroys almost 90% of their fleet. But then the fleet's commander orders the remnants of his men to keep pushing forward, and they do, meaning they end up attacking the enemy base at the same time Funeral Parlor's offensive is occurring. The UN forces face off against Arisa, one of the GHQ's Void users who has a Made Of Diamond shield, and severely injure her when Shu purges the Apocalypse Virus from the world. They also kill Rowan, though that was more a Kick the Dog moment.
Any allied army in a James Bond movie. They always keep the mooks busy while Bond goes after the Big Bad, and they always end up in possession of the field. Examples include the frogman force in Thunderball, the space marines in Moonraker, Octopussy's harem commando, and the army at Fort Knox in Goldfinger.
If the NEST Team from the Transformers films are the resident Badass Army, the conventional armed forces in the background are the Men Of Sherwood. They take heavy casualties but ultimately are vital to defeating the Decepticons.
The Europol commandos in Ninja Assassin. They don't seem it the first time they had to fight the ninjas, but when they got their act together and came prepared, things went their way.
The Fremen. Even though Paul Muad'ib Atreides was a fierce fighter in his own right, he didn't win the throne through a series of duels. He won it by having a huge army of highly-skilled, fanatical, and utterly faceless troops.
Who won against another huge army of highly-skilled, fanatical and utterly faceless troops that were until then feared by everyone in the whole galaxy.
Granted, the Sardaukar by the time of the first Dune book were arguably at their weakest due to Shaddam IV's rule and general arrogance/decadence, though they were still formidable. They're far more competent in the prequel books and Farad'n's Sardaukar in the sequels are as well (though we never really see them in action).
Interestingly, the Dune Encyclopedia provides background material that states Fremen who travelled offworld were stricken by disease and failed to adapt to humid environments.
The half-blood army of campers that Percy raises in the Percy Jackson and the Olympians books, who successfully hold the island of Manhattan against a legion of monsters.
At various times in the series, various other forces fill this role as well, ranging from B5's security troops and Starfury squadrons, to individual starships such as the Hyperion and Agamemmnon, to the combined forces of the Army of Light.
A non-heroic example: the Others in LOST. The protagonists almost always come out worse off, and whenever they score a victory it's usually because they have the element of surprise, or some other clear advantage.
In 24, the CTU response teams have only two settings: they either prove ineffective at containing the bad guys, letting them escape, or they trap the bad guys, at which point the villains get their faces wrecked.
The Knights of Camelot in Merlin fluctuate between this and a Red Shirt Army depending on the battle.
The former Tekken Force members led by Lars Alexandersson in Tekken 6. Bonus points for Lars's second-in-command being a Mauve Shirt.
The Blood Raven and Ultramarine Tactical Squads on the bridge nearing the final level in Warhammer 40000 Spacemarine. They can actually clear up the bridge of Chaos Marines and Bloodletters without you really having to do anything and can go that far without casualties.
In Mass Effect 3, the "N7 Special Ops" from the multiplayer, an unofficial coalition of individuals from across the Galaxy who've banded together to fight in warzones and aim to halt the advance of Cerberus and Reaper forces.
In the singleplayer campaign, we see examples from most of the races, fighting to defend their homeworlds, or lending support to help the others (Turian fighters providing air support for the Krogans on Tuchanka, for example).
Conquests of the Longbow has two parts in the game where you have to decide on a strategy to rescue Marian, and rob a wagon. Depending on what you pick determines both the success of that situation, AND The casualties the outlaws take on. There is one choice in each situation where the outlaws suffer no casualties.
The Azure City soldiers in The Order of the Stick tend to die a lot, but they are also more than capable of killing large numbers of goblins. In fact, if Redcloak had not used the titanium elementals to breach the wall, and created Xykon doubles beforehand, the city might not have fallen.
The metalbender cops in The Legend of Korra try to be this, but they're usually outmaneuvered and defeated handily. The Strike force assembled by Tarrlock does manage to get an onscreen victory against a Equalist base, but otherwise don't have many successes.
The lionesses of Pride Rock in The Lion King who fight the hyenas while Simba is fighting Scar.
Generator Rex: The Providence agents all show degrees of competence, like defending the great wall and mowing down thousands of insects, a battle which they win when Holiday gives them pheromones for the bugs. When Van Kleiss attacks Providence, he beats his way through them, but by the end of the episode, they fight off all his EVO mooks. When Black Knight Takes charge, they lead an Assault on Abyss, and defeat the Pack, sans Van Kleiss. Other days, they're cannon fodder, to die, or to hold off the monster until Rex can cure it.