Nightfall Series: Prince Vladimir happily does all his fighting, ruling, hunting, adventuring and manipulating himself.
The Queens of A Brother's Price don't do much, being largely retired, but their daughters are highly active in the running of the kingdom. Much of what they do is political, sitting in judgement at the royal courthouse, but two of them start off the book trying to help part of the armed forces track down some stolen experimental cannons.
Animorphs: In Andalite society, "Prince" is a military rank... so it stands to reason that princes would actually do some fighting.
Crown Prince Phillip in the Antares novels has to serve in the military just like every other Sandarian. The only special treatment he gets is that he is addressed as "Your Highness" at all times. Even when being given orders.
He even leads a boarding party in Antares Passage.
The King's Hand (basically a Prime Minister) does most of the work running the Seven Kingdoms. King Robert Baratheon, for example, did almost nothing during his reign besides eating, drinking, and chasing women.
It depends on the king. In the series, it's said that a weak king, like Robert, needs a strong hand to rule while they hunt and whore [Robert] or fast themselves to death (Baelor the blessed, also known as Baelor the Befuddled); while a strong king just needs someone who can follow orders to make sure those orders are implemented. But most kings mentioned in the series have been weak (or minors), and as such their Hands generally did the work
In 2021 of the timeline of the Axis of Time trilogy by John Birmingham, Prince Harry is quite a badass SAS colonel. After the multinational anti-terror task force he is assigned to is sent back toWorld War II, he becomes quite the celebrity in the contemporary UK.
Princess Elizabeth thinks being called 'granny' by a man old enough to be her father is a giggle, but Prince Philip is more than a little intimidated by his badass grandson.
Garion in The Belgariad by David Eddings is actually a decent king who spends more of his time as an administrator than anything in pomp and ceremony. Most other kings and royalty, and even many aristocrats, in that universe are in a similar position.
Queen Ehlana of Elenia, though she spends the first two-thirds of the Elenium trilogy in a magical coma, comes out of it hell-bent on running her kingdom efficiently; she's an exceptional ruler, and later her prince-consort Sparhawk takes on as many of her burdens as he can to help.
In the Belisarius Series, Shakuntala plans to be a future patron of philosophers besides being a martial arts expert personally, Eon is a soldier and his proudest title is "man of the regiment", Khusrau is a noted administrator and is revamping Persia's tax system and government structure, while Justinian is planning to codify Roman law. Most Malwa rulers don't do anything competently except please their overlarge and perverted appetites. Link, however, has a devious plan to Take Over the World.
Black Crown has examples of both battlefield and administrative 'doing': In 'Black Crown', two Kings are seen fighting in battle. In 'Schism', the King and his Lords are seen discussing how to run the Kingdom's affairs.
The rulers of C. S. Lewis's Narnia and Archenland are expected to be "first in every charge and last in every retreat," and also to have lean tables during famines. One gets the impression that descent is an unimportant part of being royalty: Aslan appoints a random cab driver from London the first King of Narnia. When the cabbie objects, Aslan asks him if he would remember that the Talking Animals of Narnia are free subjects, avoid holding favourites, bring up his children to do the same, et cetera. His answers are between "yes" and "A chap can't know that, but I hope I'd try," and Aslan tells him, "You will have done all that a King should do."
The Calormen royalty as well; whatever other faults you can lay at their door, are also directly involved in politics and battles. When the Jerk Ass prince (unable to leave his city because of a curse) becomes Tisroc (king), he makes peace with his neighbors, because he knows better than to let his lords win glory in battle while he's stuck in the palace - "for that is the way Tisrocs get overthrown".
Royalty in Lloyd Alexander's The Chronicles of Prydain seem to be actual leaders of the country, as well as, for the most part, badasses. A notable example is Prince Rhun, who gives every indication of being a complete doofus, but is actually an enthusiastic and kindly ruler. One of the few aversions is Fflewddur Fflam, the truant bard king with the bright yellow hair; he's a lovable fellow and not a complete doofus, but not exactly a responsible ruler. By his own admission, he's a better bard than he is a king — and he's not much of a bard. On the other hand, as a warrior he's no phony.
In Alexander's The Remarkable Journey of Prince Jen, the title character starts out as an over-pampered member of a completely useless royal family, but a series of adventures outside the palace walls, a few weeks of life as a crippled outcast, and an attempted coup make him a proper ruler.
And in The Iron Ring, the lead is a minor king from Fantasy India who abandons his country over a matter of honor; he did a perfectly good job until then and left it in good hands, but he comes back with a mega agenda at the end and reforms the country like crazy. A whole lot of other kings appear over the course of the story, as both negative and positive examples. Usurpers, jerkasses, the incredibly honorable warrior kings both human and snake, some kind of divinity, and even the king of the monkeys, who was formerly human and becomes an early party member. (Clearly influenced by Sun Wukong.)
The titular lead of The First Two Lives of Lukas Kasha is a professional layabout who's magically sent to a vaguely Persian country where he first nearly drowns and is then proclaimed king. Spends a while enjoying the easy life, then gets bit by a sense of responsibility, complains about how exhausting it is, annoys the hell out of his whole court by attempting to actually rule, and gets himself nearly assassinated. Then the plot starts.
And in the Westmark trilogy, the country starts out in a (ahem) royal mess because the King has been slacking off, while in subsequent books ruling is depicted as involving tons of paperwork and tough decisions. Alexander is pretty good at this trope generally. By which we mean it's one of his top five.
The First Lord of Alera personally goes behind enemy lines in a civil war to prematurely detonate a volcano that Kalare rigged to blow when he dies. Later he keeps the Vord Horde at bay by setting off another volcano at the capital, buying the people time to retreat.
Princep Septimus personally led his legion in many battles, including trouncing a rebellion that was starting up.
Tavi, originally named Octavian, Septimus' son, leads many into battle and engages in making peace treaties with once enemies of Alera.
Conan the Barbarian, eventually king of Aquilonia, is as much a badass after ascending to the throne as he was before. And not just with his sword: Conan also reforms the tax system, attempts to break up the large estates of the nobility to provide more farmland for freeholders (and reduce warfare with the neighboring Picts), and contributes to Aquilonian scholarship by improving their knowledge of the northern realms (including his homeland of Cimmeria). For his troubles, the nobility of Aquilonia continually conspire against him and eventually he is ousted from the throne.
Baron Edmond Talbot, from John Ringo's Council Wars series. He's very reluctantly nobility, but nobility nonetheless, and will frequently be found in battle.
Dwarven king Bruenor Battlehammer, friend to Drizzt Do'Urden, actively fights on the front lines and leads his people into battle against gray dwarves, dark elves, and orcs. A later variation has him leaving his duties in Mithril Hall to go out and hunt the monsters who threaten the nearby settlements, which leads to an argument with the captain of his royal guard about the king putting himself in danger and reminding him of his duties in Mithril Hall.
On of Drizzt and Bruenor's greatest enemies and later, reluctant allies, King Obould Many-Arrows, also takes a very hands on approach, often leading armies into battle and facing enemies in singles combat.
King Lief of Del spent the first few years of his reign traveling around his country in order to drive out the Shadow Lord's forces and free his people, and went on to rule "long and wisely".
Taylor Anderson's Destroyermen series has several positive and negative examples among the Lemurians. For actual royalty, we have Safir Maraan, the Orphan Queen of B'mbaado, who is a fierce warrior (in a culture where women don't fight) and personally leads her 600 (her elite guard) in a charge against the Grik at the Battle of Aryaal. Muln-Rolak, the Lord Protector of Aryaal, is not technically royalty (his position is more like a general) definitely fits, despite his advanced age. He accompanies Queen Maraan on her charge despite his king's objections and the fact that he has to stop several times to catch his breath. Keje-Fris-Ar, the High Chief of Salissa, also participates in battles (especially since he's not only the ruler but also the captain of his home-ship). Averted with Fet-Alcas, King of Aryaal, and his son Rasik-Alcas. Fet-Alcas is too old and fat to fight, despite the proud warrior tradition of the Aryaalans, while Rasik-Alcas, while not bad with a sword (although Lord Rolak disarms him with ease), prefers to let the others do all the fighting.
In the eyes of the Lemurians, Captain Matthew Reddy may also fit the bill, as they see him equal to any High Chief. Not only does Reddy command the USS Walker in naval engagements but he also personally commands the land battle at Aryaal (despite having no experience fighting on land).
The Discworld's King of Lancre is an example of this trope, getting involved in everything from crop rotation to the invention of the Lancrastrian Army Knife.
Although his subjects would rather prefer he didn't, and stick to kinging. Similarly, Magrat initially finds the duties of the queen dreadfully boring (it's mostly embroidering). It's a good thing the elves showed up so she could let off some steam.
Also, the Low King of the dwarves is, up till his election, a working dwarf.
The same could probably also be said of Diamond (the troll king), since he runs a 'Thud' (a dwarven/trollish board-game) Club.
The regular dwarf "kings" are even more this trope, as the term for their role might better be translated as "senior foreman".
After his marriage to Sybil elevates him to dukedom, Vimes himself qualifies; he continues to work as the head of the Ankh-Morpork City Watch in spite of being so independently wealthy that his great-great grandchildren could go their entire lives without doing a day of work. In Monstrous Regiment he's actually mistaken for a sergeant because of his philosophy that armor ought to look like it's been doing its job and his habit of avoiding committees.
Susan, despite being Duchess of Sto Helit, works first as a governess and then a schoolteacher. Her parents had spent most of their time working as diplomats outside their duchy, helping establish and maintain the peace between city-states that currently prevails on the Sto Plains.
Carrot Ironfoundersson could assert his destiny as King of Ankh-Morpork if he so chose. Fortunately for Vetinari, he believes in putting in a decent day's work, in a job where he feels he really could make a difference, preferring to be a policeman. Vetinari is happy for this agreeable state of affairs to continue indefinitely.
Doctor Dolittle: Stubbins, Dr. Dolittle's assistant, is quite surprised to learn there is more to being a king than sitting on a throne and being bowed to several times a day.
In Dragon Bones, king Jakoven does plenty of things. Sadly, those things he does also include invading countries, beating down rebellions, sexually abusing the children of the nobles involved in the rebellion, and assassinating his wife's lovers. (And no, not out of jealousy, he's gay. He does it because he's paranoid about them gaining too much influence). However, he does not do things he should be doing, like doing something about the bandit problem at the border in the south, the one where he executed lots of people after the rebellion. That's tactical intention, though. His bastard brother Alizon is later seen doing actually doing the thing, after manipulating Jakoven into giving him the opportunity to do so. Alizon is not royalty, though, being a Heroic Bastard. He does still have a rather influential position at court.
Faerie royalty and nobles very much tend to be this — and given that both Courts are frequently fighting each other as a matter of course as well as holding off the Outsiders in the background, this is entirely justified.
While not formal royalty in and of themselves, it's eventually revealed that the Knights of the Cross each have famous distant royal ancestors. It's not clear if there is a causal relationship at work here or if this is simply coincidence, but kicking butt for the Lord with the swords of Faith, Love, and Hope is certainly a large part of their job description.
Also, if he counts, the "king" of Chicago's underworld (and eventual freeholding lord under the Unseelie accords), John Marcone, certainly never shows signs of shying away from getting his own hands dirty when action is called for.
The royalty in Dune basically do nothing but scheming against one another and actually ruling their domains. Court functions and leisure occasions seem to only serve the purpose of furthering their schemes for power.
Though the Duke personally visited the mining of the Spice with a local guide to get a hands-on glimpse at the techniques.
It's actually a plot point that the Atreides family is the exception to the rule in this regard, which inspires fanatical devotion in their servants and retainers. Paul's grandfather Paulus, for example, was gored to death by a bull while trying to entertain the people of Caladan with bullfighting.
Both of the Harkonnen nephews can be pretty active. Glossu Rabban is utterly ruthless and prefers to personally execute... well, anyone who displeases him. In the prequel novels, he also leads the Harkonnen forces in an attack and flies the first no-ship. Feyd-Rautha, while not as active, does participate in gladiatorial combat (although, it's usually rigged in his favor). At the end of the first novel, he even challenges Paul Atreides to a duel that will decide the fate of the galaxy. In fact, the prequel novels are full of aristocrats actually doing things, including Paulus Atreides and Dominic Vernius.
And in general, most nobles - including the Harkonnens - are shown to have a hands-on approach to government, spending as much time with statecraft as they do with leisure. One of the first scenes of Dune: House Atreides has the Baron Harkonnen himself doing the same sort of inspection of a spice mining operation that Duke Leto did in Dune, both to ensure that everything is being done smoothly, and to better understand how he's making his money.
Legends of Dune also has some nobles taking a pretty active role in governing and military command. The most notable is Xavier Harkonnen. His first appearance has him defending Salusa Secundus from a Cymek attack in a Space Fighter. His grandson Abulurd was also a capable commander.
At the end of The Navigators of Dune, Emperor Roderick Corrino forces all the nobles in his court to go to a remote village on Salusa Secundus to personally help out with the recovery efforts after a devastating flood. His intent is to make this trope true, after his brother Salvador's incompetent reign. Roderick's own wife Haditha is in charge of the relief efforts, wearing boots, coveralls, and gloves, and Roderick makes it clear that, unlike his brother's wife, Empress Haditha will be extremely involved in the day-to-day running of the Imperium. This is compared to the garishly-dressed nobles, who are afraid of getting their fancy clothes dirty. There are, however, exceptions, such as the newcomers Willem Atreides (who had a normal job back on Caladan before his brother's murder) and Danvis Harkonnen.
In the Enchanted Forest Chronicles, Cimorene moseys from Rebellious Princess at the beginning of the series to this trope in the second half of the series, maintaining the same (high) level of practicality all along. King Mendanbar can and does perform pretty much every significant task in his territory himself. His "court" is a handful of palace staff that takes care of daily operations. The new King of the Dragons, crowned at the end of the first book, also operates firmly under this trope.
Mendanbar was actually taking this trope to unhealthy extremes when he was first introduced, as Cimorene and Morwen both pointed out. One guy and his castle staff can't run an entire kingdom and the attempt was running Mendanbar himself ragged. As Cimorene had helped the Dragons set up a system of delegated authority it is presumed she did the same for the Enchanted Forest as well.
Most of the royals (and other rulers) in the Emberverse fit this trope. Norman Arminger (the Lord Protector), Mike Havel (Lord Bear), and Astrid Larsson (the Hiril Dunedain) are war leaders; Juniper Mackenzie (the Mackenzie of Clan Mackenzie) is a combatant, a High Priestess, a musician and an expert weaver; Mathilda Arminger and Rudi Mackenzie (their parents' heirs) undertake a quest and fight in combat in the later trilogies.
All of the Thanes in The Godless World Trilogy are this. It ranges from leading in battle to being an efficient administrator. This re-enforced by the fact that oaths are taken very seriously. This does not preclude advisors or wealthy merchants mucking up the works.
In Harry Potter, the Pottermore'' website says that goblins select their kings by smithing skills: "in goblin culture, the ruler does not work less than the others, but more skillfully."
In the Hell's Gate series, this describes the Calirath dynasty of Ternathia, whose male heirs are required to learn how to be soldiers. Nor are the princesses expected to simply sit around and look princessy.
Every ruler of Valdemar fits this, as the rulers are required to also be Heralds, and the Heralds of Valdemar do whatever the kingdom requires of them, from fighting and spying to policing and judging.
Although the royal family of Valdemar unhesitatingly serve as warrior kings (or queens, or princes/princesses, etc.) when necessary, they are still the only Heralds who are under the injunction to stay out of danger whenever possible. Elspeth had to resolve the conflict between her conflicting imperatives as heir ('avoid any avoidable danger') and Herald-Mage ('you are an incredibly rare strategic resource, the very tip of the spear') by abdicating her position in the line of succession to concentrate on her battle-mage duties.
All of the male nobility of The Reynard Cycle are expected to be warriors, as well as serve as the judicial authority of their domains. When the men are off to war, or when a woman inherits a title due to not having any brothers, women are expected to serve in the second capacity, and act as military strategists if not participants.
The Empress of Taysar in the Spaceforce novels genuinely governs an extensive galactic empire, ruling as absolute monarch. At least one of her sons, Prince Ragoth, regularly engages in diplomatic missions with other galactic powers.
The Hollow Kingdom Trilogy's elf and goblin Kings fit the trope very well. They cast and maintain the spells that protect their kingdoms and make choices for the good of their people, even at their own expense.
Kate does well in the first book, too. Her crowning glory is breaking out of the kingdom to go on a manhunt for the sorcerer who's been stealing goblin souls in the second half, though she's also mentioned to work as an English tutor for the goblins.
Due to Manticoran royalty in Honor Harrington being very much based on the British one, it's not all that surprising that they Actually Do Something, and they do it a lot. Especially since a Manticoran monarch has significantly more weight in the daily running of the shop, being a kind of a hereditary President in a semi-presidential republic. This also goes down the line, with Michael Winton, the younger brother of the current Queen Elizabeth III, and Michelle Henke, her first cousin, being serving officers in the Navy and all that. Elizabeth's own son and heir apparent is also going to the navy soon — it's a family tradition actually, much like their originals.
Part of the backstory of the origin of the Manticoran government was that the system was set up so that the heir to the throne was constitutionally prohibited from marrying someone coming from the nobility/aristocracy: this meant that heirs always were the daughters or sons of people whose families actually had to work for a living, and hopefully picked up that habit. This also helps prevent inbreeding common to many Real Life royal families.
The nobility also get in on the act. Plenty of them choose frontline military service, including Michael Oversteegen, Michelle Henke, Gervais Archer, and Admiral White Haven himself.
Queen Berry of Torch hasn't borne any children yet, but has already vowed that when said kids show up, they will follow this trope.
Being elevated to the rank of Princess of Oz when she moves there permanently doesn't slow Dorothy Gale too much.
Ozma may count, while in most books she basically just sits on her throne while Dorothy and the others go on quests, but in Ozma Of Oz, not only does she personally lead a group of adventurers to rescue Dorothy from Princess Langwidere, but also to the Nome King's kingdom to rescue a group of missing nobles. Even further if you count Tip, her male alter ego who is very adventurous before regaining his true form and having the responsibility of ruling a kingdom
In Tin Man her granddaughter (and Ambrose) were holding off a coup from Azkedellia. They may have lost the coup, but Possessed!Az was a pretty efficient tyrant. Then the second Dorothy, DG, shows up...
Prince Garric and his sister Princess Sharina from David Drake's The Lord of the Isles series are an absolute nightmare for their bodyguard regiment because of their insistence on being in the thick of things - which is often pitched battle. The guards have the dubious compensation of knowing they're now shielding royalty who're worth protecting.
A Mage's Power: Princess Kasile of Ataidar is well known for her social activism. She also has an eye out for threats to her family and crown. In fact, one of the titles for the monarch of her country is "The Highest Public Servant".
In the Malazan Book of the Fallenverse by Steven Erikson and Ian Cameron Esslemont, Malazan Emperor Kellanved was a powerful sorcerer who researched and travelled in his quest to become a god. He succeeded. Before launching his extraordinary plan and forging his empire (magnificently so - for around 90 years or so), he apparently used to run a bar for a while.
Empress Laseen, who succeeded him, was the former head of the Imperial assassins.
Prince Roger(Etc) MacClintock of David Weber and John Ringo's March series was a very lazy royal (one of the reasons everyone hated him). He quickly changed. At one point he planned to spend his life lifting the Death World Marduk out of the dark ages; now he is planning to do this to the entire Empire, which has been taken over in a coup in which one of the first steps was to strand him on Marduk, where he Took a Level in Badass just to survive.
In Masques, the young king is very eager to be a royal who does something. He aids the refugees who have fled from the Evil Sorcerer who seeks to take his throne, and is always seen walking through the rebel camp, dispensing advice and doing work. Ironically, the fact that he is so invested in helping his people might be the main reason why the Evil Sorcerer seeks to dispose of him - he gets in the way.
In Robert Asprin's Hit or Myth, the King of Possiltum grows tired of his daily regimen of arbitrating his subjects' legal hassles, and attempts to permanently foist off the job on his court magician Skeeve. (Also, he was being unwillingly herded into a diplomatically advantageous marriage, which is another reason not to envy working kings...)
Magic in Garth Nix's Old Kingdom trilogy is very much In the Blood. Therefore, in addition to Queen Sabriel's duties as Abhorsen, keeping the Dead dead, King Touchstone I has the responsibility of ruling, restoring order and peace, and fixing the broken Charter Stones, which keep the Kingdom safe to begin with. The latter activity alone takes years off his life.
Patriot Games makes a big thing out of Prince Charles's time in the Royal Navy, and has him being a competent seaman, running around shooting bad guys, and generally being badass. The Duke of Edinburgh is portrayed in the same sort of way, although on a much smaller scale as he plays a much more minor role in the story and doesn't get to shoot anyone.
Princess Mia in The Princess Diaries puts out in the open a document that had been hidden away that declared that Genovia is supposed to be a Democracy, jeopardizing her entire family's claim to the throne of Genovia and forcing her father to run for election when he had already been ruler. But Mia does it anyway because she genuinely wants what is best for the people of Genovia.
Queen Tamra, and later King Bruno, in Wil Mc Carthy's Queendom Of Sol series. Tamra takes an active part in handling threats to the system, and Bruno is a super-genius physicist who CANT stop working. The irony is that they are SUPPOSED to be Authority in Name Only, but it doesn't work that way, due partly to the genetic quirk impelling Homo Sapiens to bend at the knees (which was the reason for reviving monarchy in the first place) and partly to the forceful personalities of the incumbents. Their "royal decrees" have no authority, but almost everyone obeys them anyway.
In the Rainbow Magic series, Queen Titania acts as a mentor to the girls, and her magic makes whatever Jack Frost stole appear close to Rachel and Kirsty.
King Oberon once used his crown to teleport Jack Frost to his throne room and prevent him from causing further mischief.
In The Red Vixen Adventures most foxen nobles spend their time administering their holdings and dealing with the concerns of Commoners in their domain. With a strong sense of noblesse oblige. Though there are exceptions such as Countess Highglider who sabotages the holdings of her vassal House Darktail over a petty grudge.
Nearly all nobles in The Riftwar Cycle, no matter their planet of origin, are like this. The primary setting, the Kingdom of the Isles on Midkemia, is particularly notable because it works under a feudal system called "The Great Freedom" which gives nobles a responsibility to go out and defend their people in exchange for their allegiance.
Prince Arutha is an exceptional example—he is depicted as far more interested in being hands-on than delegating the dirty work to his subordinates. At one point, he even fakes his own death so he can get away from his princely duties so he can sally forth and kick a whole lot of ass.
The nobles of pan-Asian Kelewan can vary. Some are more or less useless, others very hands on. Some are warriors, some accountants, some spoiled dandies. The fortune of their estate rises and falls with their various abilities (and those of their advisors) so this is mildly deconstructed.
It becomes a Discussed Trope a few times, with Gardan pointing out that he is somewhat wasted as Duke and Knight-Marshall of Krondor, in that a man of adventure like Arutha should have an administrator rather than an Old Soldier as his right-hand man. Really, he just wants to retire.
The heads of the eponymous three kingdoms from Romance of the Three Kingdoms also count. Liu Bei, in particular, wove straw mats and sold shoes before he entered politics and military service. In fact, once any noble stops being one of these and starts simply reigning, an ambitious adviser will usually pick up the slack and eventually supplant him.
In John Woo's movie adaptation, Sun Quan the King of Wu fights on the frontlines during the Battle of Red Cliff. This certainly never happened in real-life; it didn't even happen in the historical novel!
Not that battle, no, but Sun Quan is actually rebuked by his subordinates for spending too much time near the front lines in other battles.
Most royals in David Weber's Safehold books are competent leaders who watch over their lands to the best of their ability. However the most notable are the Ahrmahk dynasty of Charis. In the first book, both King Haarahld and Crown Prince Cayleb lead their forces into the ultimate naval Curb-Stomp Battle. In the third book, Cayleb also personally leads the forces that attack Corisande.
Queen Shulamit in The Second Mango is constantly reading up on new topics so that she can make informed decisions about how to rule her kingdom. She also directly solves crimes and mysteries with the help of her partner and friends, Agatha Christie-style. Prince Kaveh (from the book's sequel) also counts, as he directly helps instigate a worker's revolt against unfair labor conditions.
The Royal Family in Kiera Cass' The Selection. The family is consistently shown to actively rule and Prince Maxon takes his role as the future King very seriously. It also becomes increasingly clear throughout the story that if she were to become Queen, America would be this type of ruler.
Seraphina has the Goreddi royal family: Queen Lavonda put her life on the line in her youth to negotiate a peace with Ardmagar Comonot, trekking up a dangerous mountain pass with only two young guides, and she continues to put a lot of energy into keeping peace with the dragons for the next forty years; Glisselda learns everything she can about how to run her future kingdom and declares war on the Tanamoot when they've already broken the peace; and Kiggs is a military captain with a reputation for investigative talent.
Princess Raisa actively invokes this trope throughout The Seven Realms Series. In book one she founds the Briar Rose Ministry, a charity she and her father run that earns money for the people. The Briar Rose ministry not only helps some of her people avoid starvation, but gets some younger people the money they need to go to school and earns her a very loyal following. (This becomes a very important plot point later on.) By book three, she stops caring about making enemies within the government and goes around rectifying serious issues with the way things are done in order to help the people. A good portion of book three is spent on showing her doing this.
Though it's mentioned that at least one Highprince leads from the rear, with his Shards being bestowed on the Highprince's Champion.
Pretty much everyone, both male and female, no matter their age, in Tales of the Branion Realm. The rare exception is a sovereign who prefers to go into common taverns and drink, but everyone else does something, usually but not always killing things - his five-year-old heir presides over heresy trials.
The former king in The Talisman,the twinner of Jack's father, was a man of the people who traveled around to address those people. The current queen would be as well if she weren't really busy at the moment with the whole dying thing.
The kings of Tortall in Tamora Pierce's series are required to become knights and undergo the Ordeal of Knighthood (more or less a Mind Rape that makes you face your worst fears) and a few characters comment that King Jonathan and his queen Thayet very much pull their weight in several areas.
Jonathan and Thayet, in particular, have been responsible for such an insane amount of social progress in a few decades that at times it tests the bounds of Willing Suspension of Disbelief. It also seems that Thayet has expanded the role of the queen in government — she's officially Jonathan's co-ruler, and it's implied that this was not the case with previous queens. Among other things, she's started up the Queen's Riders, an unglamorous, coed branch of the military that goes around cleaning up Tortall in cases where the (all-male) King's Own would make a hash of it by being so big and bright and shiny. She's its official commander and is actively involved in what it doesnote to the point where she once left a state banquet, wearing a very expensive Pimped-Out Dress, to go to the rescue of a Rider group in trouble. Jonathan asked her to please change next time.
Tamora Pierce seems to like this one. In her Emelan books, we see His Grace Duke Vedris IV of Emelan taking a hand in public welfare and offering his castle as protection for a family whose members are being systematically murdered, Empress Berenene dor Ocmore of Namorn building up her country, making it powerful, wealthy, successful as well as fighting wars to keep it that way, not to mention shrewdly manipulating her nobles so as to keep them from making too much trouble (even if she is a magnificent bitch. And then there's Lady Sandrilene fa Toren, who while not royalty is close kin to the two mentioned above (and there is reason to believe that the Duke may well make her his heir) and is ready to face down armies armed only with her noble blood and springs to battle the moment she sees anyone being mistreated, leading to many a Crowning Moment of Awesome in the series.
She even does it with her evil royals. Duke Roger of Conte is noted for his magical research and knowledge, and he was also a famed amateur jeweler. The King of Tusaine does nothing, but his two brothers are his lead general/guy who mostly runs the kingdom and a top spy respectively. Both of these are in the Song of the Lioness quartet. And in the Immortals Quartet, Emperor Mage Ozorne has that title because he's so well known for his work in magic.
A lot of the royals in the Trickster books do either 'nothing' or 'nothing except plot to murder one another,' but our heroine is working to depose them. The original rebellion-queen-candidate is beautiful, brave, charismatic, and fairly clever, but not a practical individual; after she runs away with a boy they use her sister, who is presented by the story as a far superior choice as she is brilliant, pragmatic, and tough as nails.
Emperor Ozorne of Carthak was a shrewdly manipulative individual and powerful mage who put most of his effort into creating as large an empire as possible. His heir Kaddar (though Kaddar doubted he'd survive long enough to actually inherit the title) was a hard-working student who hoped to find a way to end the droughts his country was suffering. When he does take up the title he seems to do a lot for getting the country back in order.
Luxa from The Underland Chronicles. More so as the books go on, especially when almost the entire Council is killed in the war.
In Vorkosigan Saga, the chief job of Vor, like most aristocracies is war. However in modern times the Barrayaran forces have plenty of commoners in the officer class (In fact, Barrayaran tradition holds that a commoner who serves twenty years in the military and retires with an honorable discharge is the social equivalent of an untitled Vor). Other duties seem to include judging disputes and investigating crimes and maintaining a paternalistic rule over their respective districts. The Vorkosigans themselves are close enough relations to the Imperial dynasty for Aral to be one time suspected of Imperial ambitions. They conduct social reforms, engage in parliamentary politics, take part in espionage and covert warfare, and improve their own local desmene.
Emperor Gregor is not known for just sitting around, either. This was a problem at one point....
Subversion: Emperor Varnazd in Yulia Latynina's Wei Empire cycle desperately wants to be this, but almost everything he ever does to that end (and he tries a lot of things) backfires badly, to the point of directly causing an all-out civil war.
Annoying though Elayne Trakand can be, she spends a fair amount of her time as princess chasing evil sorceresses around the known world and kicking butt. Then she ascends to the throne and immediately has to fight a civil war.
Rand has plenty of things he needs to do as the Dragon Reborn and being crowned king of Illian and more or less being in charge of several countries he has taken does not change that. The books do show him less and less though as time goes on so while he is probably pretty busy king and ruler, it can seem like he isn't doing much to the reader.
The series as a whole varies greatly with respect to this trope. Before the main characters come into their own the nobility of some nations are shown as effete, vain parasites devoted to jockeying for position in court - Cairhein especially, where a previous king caused a disastrous war with a Proud Warrior Race just because he wanted to use some really, really rare wood for his new throne - but for many others, royalty is hard work. For all the northern rulers, keeping the Blight back is a full-time job. The Seanchan take very seriously their obligation to provide peace and justice in their territory - they'd be the good guys, if not for treating channelers like animals, and it helps them that their invasion happened to start with nations with very weak rule of law until they showed up.
In the historical novel Wings of Dawn: Well, nobility who actually do something. Though once Lord Hawkwood manages to get Queen Isabella involved...
Xanth has several goblin chiefs, every miscellaneous species of royalty, and almost all named human royalty; also, as of Yon Ill Wind, the Demon X(A/N)th qualifies.
Most notable is Princess Ivy, who at the age of three forces the most powerful dragon to become her best friend, raises the good magician's son to competence and beyond, and prevents a wiggle swarm from destroying all Xanth with only said friends This would also count as Badass Adorable.
The kings and queens of Wellakh in Young Wizards appear to be a very long and unbroken line of wizards, who by definition do rather a lot.
Just as in Real Life, in 1632 there's Gustav II Adolphus, king of the Swedes. Either on the front lines or commanding the army in multiple battles, and once even making a reckless charge to save his uptime allies, in the first book.. Seems to be what he likes as he sent Axel back to Stockholm to manage affairs of the kingdom in 1634: The Baltic War.
Many of Bernard Cornwell's novels set in earlier time periods, such as the Grail Quest or Warlord Chronicles trilogies, involve monarchs heavily involved in government, and, particularly, warfare, as is appropriate for the time. A somewhat unusual example is Alfred the Great as he appears in the Saxon Stories, often described by the Unreliable Narrator as engaging in useless clerical or religious work rather than acting as a military leader, evidently unaware that such work will have as great an impact on English history as any of his battles.
From The Lord of the Rings there's Elendil, Gil-Galad, Aragorn, Legolas, and the whole royal house of Rohan.
In The Silmarillion, all the Noldorin princes are warriors who go to battle against the Dark Lord, and most of them die that way.
The best example is undoubtedly King Finrod Felagund of Nargothrond (say it ten times fast), who even abandons his kingdom to his brother and leaves with a few volunteers after his people refuse to help him rescue the human whose father saved his life, because he swore an oath that he would repay their family.
Fëanor was also a king who actually did some things. Pretty insane, horrible, evil things, mind, but things nonetheless. And he certainly wasn't staying at the rear in battles — in fact, that's what killed him.
Fingon, who rescued Maedhros from Thangorodrim; Beren and Lúthien, who pinched a Silmaril from under Morgoth's nose; and all the characters who are the descendants of Húrin and Huor.
Fingon's father, High King Fingolfin, not only led his people in battle but challenged Morgoth himself to single combat. He lost, and he died, but he also permanently crippled Satan's foot and humiliated him in front of his troops.
If the similarity in names wasn't a clue, pretty much all the above are quite closely related. Fingolfin is Fëanor's half-brother, and Finrod is the son of Finarfin, who is Fingolfin's brother. Speaking of Finrod, we may as well mention his sister ...
Galadriel, who is the oldest of the Noldor royalty still standing, has undertaken quite a few actions against Sauron (although they are generally 'off camera'). Actually, even when at home, she is in constant battle with Sauron through sheer willpower. She was also pretty scary during her youth; she was one of the leaders of the rebellion of the Noldor (although she wasn't directly involved in the Kinslaying) and was subsequently banished from Valinor. One of her older names was Nerwen, meaning "man-maid", a reference to both her height and her general badassery.
This is especially true in the Lord of the Rings movie. Watch through the Battle of Pelennor Fields for a Mûmak death count — of those onscreen, one of them is taken out by the Dead Men, and only one is taken out by a member of the Fellowship (that would be Legolas, who takes a good minute and a half to do so). Then Théoden kills one (well, leads the killing of one), Gamling kills one (close enough), Éowyn kills one, and Éomer kills two. With one thrown spear.
In The Hobbit, there's Thranduil (the Elvenking), Thorin Oakenshield (King Under the Mountain), Fíli and Kíli (Princes of Erebor), Dain Ironfoot (their next-closest cousin and heir) and (future human King) Bard I. During The Return of the King, Bard's grandson Brand and Dain died fighting in the attack on Erebor and Dale. Their sons, Bard II and Thorin III run off the enemy army after the fall of Sauron.
Bard was pretty much made King of Dale because of him actually Doing Something in The Hobbit. His off-to-the-side actions during the War of the Ring are the trope played straight, though.
Elrond was impressive, too. Sure, by the time Sauron was off kicking everyone's shit around, he wanted to abandon Middle-Earth, but look at what he did the first time it happened. Hell, it isn't an example of the king being badass, but even being willing to take his people and abandon their slice of Paradise the second time around is an example of a royal willing to make hard, painful decisions. You don't always have to be a fearless warrior guy to be an active leader of your people.
Elrond had proven his badassery in the Second Age: he was Gil-Galad's officer on the spot to deal with Sauron once Ost-in-Edhil fell (Rivendell was founded as a refugee colony, and promptly beseiged). He was later involved in the War of the Last Alliance, and ended up commanding the Noldorin contingent after Gil-Galad's death.
Thrór, Thráin, Thorin, and Frerin might also count: they all worked as smiths, since they're in exile because of a large red dragon.
Thorin's cousin, Dáin II Ironfoot, who leads the dwarves of the Iron Hills into the Battle of Five Armies when Erebor Calls For Aid. Dáin later dies defending the gate of Erebor when Sauron sends armies through the north.
And does so standing over the body of King Brand, who'd already gone down swinging.
There was a short story where one royal family would have the next heir to the throne go on a trip down "the Prophet's Road" on their twentieth birthday. What happened to them would influence their rule; the protagonist's grandmother nearly starved to death, so she had granaries made and stocked. His father was attacked by bandits, so he built up the guard to insure his people were safe. Said father even says that what separates a person who simply holds the title until the next and someone who goes down in history is what they do.
Lissa Dragomir from Vampire Academy is a royal Moroi, certainly a big part of the story and doesn't sit around. She helps break Victor Dashkov out of Tarasov prison in Spirit Bound, her spirit powers being the key element of the plan. She trains on how to stake Strigoi and manages to use her training on Dimitri to bring him back to his former dhampir state. She is part of the plan to break Rose out of prison in Last Sacrifice and works hard to Clear Her Name by investigating the murder of Queen Tatiana Ivashkov.
In Noob, the Non-Player Character faction leaders of the Coalition and the Order are shown taking a role in active combat. The Coalition's is the most powerful human character (only the Physical Gods are more powerful than him) and used as The Worf Effect to show the extent of Tabris' power when the latter is introduced. Keynn Lucans from the Empire hasn't been seen doing much by comparision. However, considering that he's the Bio-Augmentation-enhanced leader of the technology-oriented faction, Arthéon speculates that messing with him is the last thing a reasonable person would want to do.
In The Shattered Kingdoms, the Nomas seem to have a rather more relaxed view about kingship than other cultures, and Jachad has no problem heading off into a warzone all by himself to take care of things. (Of course, he has his magic.)
Perry Rhodan, main character in the seriesPerry Rhodan is only able to make the solar imperium, with the Earth at its core, because he is a total Badass, also Authority equals asskicking
In the Dreamblood Duology, Eninket, the Prince of Gujaareh, is more than just a pretty figure on the throne. He cares about his people, and especially about his Royally Screwed Up by tradition family. Unfortunately, he is willing to use rather sinister means to achieve his well-meant goals.
In The Witchlands, both prince Merik and princess Vivia Nihar are officers in the Nubrevnan navy, and it's shown many times that it's not just for show.
In Tales of the Magic Land it's emphasized with Scarecrow and the Iron Woodcutter (considering it's a Soviet fantasy and sovereigns needed to be really cool to get acceptable for the readers), as opposed to their predecessors the Wicked Witches. Scarecrow constantly thinks of ways to modernize the Emerald City (including turning it into an island that proves very useful during sieges), and the Iron Woodcutter constantly takes part in hard labor such as road building.
Mouse Queen Ramina also is quite an Action Girl, as she is always the leader when the mice go to battle. Not to mention the fact that she's a good witch who often helps the heroes.
A borderline example: for all his faults, Urfin Jus did teach the Leapers to use fire, cook food and build better houses, even if it all was for his own goals.