Sojiroh Nichikado of Hana Yori Dango serves this purpose in his family; his oldest brother left to become a doctor and is considered the black sheep of the family, while Sojiroh stayed behind to train to take charge of his family's tea ceremony enterprise. However, while he's not the protagonist, he's a far more important character than his never-seen brother, and is a flagrant hedonist and womanizer.
Similarly, his Korean counterpart So Yi Jung in the Boys Over Flowers K-Drama. Though the family is into traditional pottery instead of tea ceremony, and he's given a more sympathetic approach.
Illumi of Hunter × Hunter, the perfect emotion-impaired first son of an assassin family, is quite baffled by his little brother running away from home and talking nonsense about making friends and not wanting to murder people for money anymore. However, he remains convinced that it's just a phase and Killua will calmly return to the family business eventually.
Milluki, Killua's other older brother, fits the other part of this trope. He doesn't understand why his father and grandfather still favor Killua (the unofficial heir, despite being a rebellious middle child) over Illumi and him, and heavily resents his younger brother for this. He eagerly accepts the responsibility of disciplining Killua with chains and whips. Ironically, Milluki himself is a failure of an assassin (essentially a Fat Bastard otaku geek) according to the rest of the family (though he obviously thinks otherwise).
Witz Su from After War Gundam X is supposed to become one of these after his father and younger brother die and leave him to care for his very numerous family (mother, three sisters, one brother). However, Witz runs away from home and becomes a Gundam pilot, something his mom is very upset for, and doubly because she hates mobile suits. He gets to go back home with his girlfriend, Toniya, so it's hinted they've made amends.
Yukifumi "Yuki" Todou from Sensual Phrase is supposed to continue with the family tradition, which is Noh acting. He becomes a rock musician instead, and is even disinherited. He returns to acting when Aucifer is disbanded.
Muramasa Kaburagi, Kotetsu's older brother, from Tiger & Bunny, who runs the family liquor store and occasionally takes care of Kaede while Kotetsu is out being a superhero.
Jeremy from A Cruel God Reigns endures physical and sexual abuse from his step-father so that his mother can be happy in her new marriage. He even goes to the lengths of begging Greg not to tell Sandra when he threatens to expose them when Jeremy won't do exactly as he asks, as he fears that Sandra will attempt suicide (again.) In fact, if he hadn't done that, Sandra and Greg would not have gotten married in the first place. His role of being The Dutiful Son is what causes Jeremy's Trauma Conga Line and Deus Angst Machina.
When Hal Jordan joined the Air Force against his mother's wishes, she forbade him from seeing her until he quit. Hal's older brother Jim eventually had to quit college and return home, which only got worse as his mom developed cancer. When Hal was dishonorably discharged, Mrs. Jordan has already died and Jack nearly beats up his brother for making their situation happen.
In Uplifted Rael'Jarva, growing up he was the model of what the future Quarian ideal would have become had the fleet not intervened in World War II.
One subplot in The Good, the Bad and the Ugly involves Tuco chastising his brother for staying home and taking the easy road by becoming a priest, whereas Tuco chose what he felt was the only other profession available to them: a bandit. (Tuco might have gone easier on his brother had the latter not had such a disapproving, condescending attitude to him and his activities.)
In Star Wars: Return of the Jedi, Luke seems to think that Leia is this. Luke himself is actually this himself, to an extent; he really wants to leave home in A New Hope, he's legally an adult and could leave without his aunt and uncle's permission, but he just won't, to the point where in the radio drama he argues angrily with a friend who wants him to just cut and run. It takes tragedy to get him to go.
Early drafts and one printing of the RotJ novel indicate that originally Owen Lars was supposed to be this for Sibling Yin-Yang with his brother: Obi-Wan Kenobi.
It's a Wonderful Life is unusual in that the "prodigal" son is actually an Ace Pilot war hero who idolizes his older brother. Largely owing to the fact that said elder brother saved his life when they were kids and made an absolute ton of personal sacrifices that allowed him to become a war hero in the first place.
In the Steve Martin vehicle Parenthood, his prodigal brother that his father always preferred turns up and turns out to be as useless as ever, teaching his father the value of Martin's more dutiful ways.
In the 2011 film Warrior: What Tommy sees Brendan as.
Alfred in Legends Of The Fall always plays by the rules and does everything he can to try and make his father proud, but knows (and resents) that he will never measure up in daddy's esteem to Troubled, but Cute wildchild Tristan. Interesting play on the trope as described above in that in the end, Alfred leaves the family farm while Tristan spends more time at home on the ranch.
Both Cersei and Tyrion Lannister see themselves as this. Their father Tywin however favours their brother Jaime, who ironically doesn't want to be Tywin's heir.
In a case of a dutiful brother rather than son, Stannis Baratheon obeyed and served his older brother Robert not because he wanted to, but because he considered it his duty as a younger brother. This included defending Robert's castle of Storm's End at great personal cost to himself in order to put Robert on the throne. Robert repaid Stannis by giving Storm's End to their five-year old brother Renly and instead giving Stannis Dragonstone, a useless rocky island.
In Death Comes as the End, the eldest son Yahmose makes a plodding, responsible, henpecked contrast to his womanizing, hard-drinking brother Sobek and their spoiled little brother Ipy. Yahmose snaps after repeated taunting by his father's new concubine, committing several murders, beginning with the concubine.
In A Pocketful of Rye, Percival Fortescue makes a dull, respectable showing against his dashing younger brother Lance, the family Black Sheep who was kicked out of the family business years ago.
Lindsey Davis' Marcus Didius Falco; his older brother was a Loveable Rogue who got himself killed in battle by being too dashing to wear his helmet properly, after which Falco cleaned up the messes his brother left behind (see especially Poseidon's Gold).
Granny Weatherwax in Terry Pratchett's Witches Abroad. She claims that after her sister Lily left, she had to stay and be the good one. She didn't seem particularly happy about this either. She probably would have been the good one anyway, but what she really wanted was the opportunity to choose, which Lily took from her.
Regulus Black as recalled by his brother in Harry Potter and the Order of the Phoenix. Subverted, because in the Black family, this meant that he became a Death Eater while the 'shameful' one, Sirius, joined the Order of the Phoenix.
Percy Weasley in the first four books: prefect in his fifth year (Philosopher's Stone), Head Boy in his seventh year (Prisoner of Azkaban), followed by the career his mother Molly approved of in the Ministry of Magic (Goblet of Fire) - but his no-nonsense attitude give him trouble with his family: Molly sang his praises throughout the first four books and seemed depressed when he walked out on the family.; with Arthur, it's more a matter of absentmindedness than outright favoritism, and his siblings do love him but are peeved by his attitude (specially the very chaotic twins.) (He even has a Face-Heel Turn, but returns home in Deathly Hallows just in time for the last battle)..
Sostratos in Over the Wine-Dark Sea by Harry Turtledove. He is a respectable young man who gets along well with his father and younger sister. When he goes to sea as supercargo in the Ancient Hellenic merchant galley Aphrodite, he is always beside himself trying to keep the captain, his cousin Menedemos, from getting into trouble and hurting the family business.
Danny Saunders in The Chosen is like this. He does not follow this plot and feels no jealousy toward his brother. But he is a very dutiful son especially considering his rather "rigorous" upbringing.
Benjamin in Never Wipe Tears Without Gloves starts out as the dutiful son and a very promising Jehovah's Witness. This makes it all the more difficult for him to come out of the closet.
Dean Winchester obeys his father John without question and berates Sam for questiong his orders. Dean is just as capable of being a dutiful brother and as shown by "What Is and What Should Never Be", tends to idolize Sam. But it was revealed by the shifter in "Skin" that he/Dean does resent Sam for getting to leave. Dean also manages to combine this with Troubled, but Cute.
Michael is this Up to Eleven. Of course, Dean's relationship with John and Sam mirrors the relationship between Michael, Lucifer and God. As it is in heaven, so it shall be on earth and all that.
A variation happens in the SitcomWings. Brian and Joe's mother ran out on the family when they were little, and their father... well, <wigflip, cuckoo>. So, anyway, Joe had to step up as a child and be The Dutiful Son; as he pointed out later when he ranted to his returned mom: "You left me to take care of two little kids, Brian and Dad!"
On General Hospital the extremely rich and equally screwed up Quartermaine family had Ned Ashton who was constantly trying to appease his grandfather and cover his cousin's screw-ups. He eventually left town simply because he got tired of it.
Cesare Borgia goes above and beyond. He starts off by helping Daddy Rodrigo become pope, saves his life within the first two episodes, and refuses to leave his side even when the French are invading. All of this despite the fact that his father is forcing him to become a cardinal while giving his Too Dumb to Live brother the military position Cesare has always wanted and would most likely excel at.
Judging from what we've seen of season 2 so far he's over the whole dutiful son thing.
Stargate Atlantis: John Sheppard's brother in "Outcast", who stayed behind to take care of the family business while Sheppard was out on military ventures across the world after having a fallout with his father. They eventually manage to reconcile after their father's death.
David from Six Feet Under stayed to take care of his family's business while his brother Nathan went away not wanting to work with dead people.
Stefan from The Vampire Diaries. Part of the reason why Stefan was the favoured child with Giuseppe was because Stefan was a dutiful, responsible, obedient son.
Dinosaurs: Back when they were kids, Earl and his sister Pearl dreamed of being singers. However, for the sake of his sick mother, Earl set the dream aside and resented his sister for not doing the same.
Doug Hammond in Political Animals. While his drug-addicted gay brother and philandering father constantly draw the family into the tabloids and wreak havoc on his mother's political career, long-suffering Doug struggles to be the responsible one.
Nessarose from Wicked. When Elphaba becomes a rebel, an outcast and an activist, Nessa takes over her father's position as governor of Munchkinland. However, Nessa eventually also becomes a wicked witch, and goes Yandere for Boq.
King Edgar, ruler of Figaro, is like this in Final Fantasy VI. After their father is murdered by the The Empire, Edgar's twin brother Sabin is so angry and upset that he can't take it anymore and wants to strike out on his own. Edgar tries to remind him of their responsibilities to Figaro, and what would happen to the kingdom if they both left. Sabin doesn't want to leave the kingdom hanging, but his desire for freedom is so overwhelming that it's tearing him apart. Edgar eventually proposes a coin toss, where the winner will go out on his own with no regrets. It turns out that Edgar rigged the coin toss so that Sabin would win either way, but this method allowed him to leave with a clear conscience.
Gamlen paints himself as this in Dragon Age II because he stayed and took care of his and Leandra's elderly parents while Leandra spent years on the run because of her husband's status as an unregistered mage. Of course, this doesn't justify his later cheating her out of her inheritance, or his making deals that force her kids into indentured servitude for a year.
Zalanna of Ears for Elves fits this trope very well, and wishes everyone else did too. Sometimes she lectures Tanna about it: "As daughters of the founding families, it is our duty- nay, our birthright to set an example for the common folk."