The A-Team: Col. John "Hannibal" Smith, the A-Team's leader, can fall under this. He smiles at Murdock's antics like a parent watching their young child act out fantasies, he can keep B. A. under control, and he reminds Face to keep his wandering eye in check and focus on the task at hand. Hannibal also has this cute habit of referring to the other members of the A-Team by their military ranks (Captain, Lieutenant, and Sergeant, respectively), even though they've all technically been discharged, and they often refer to him as "Colonel." He also always has unwavering faith that his men will get the job done, and his nerves of steel are more likely to be rattled by something threatening Face, B.A., or Murdock than something threatening him.
Played straight by Richard Winters, where due to his leadership and exceptional concern for them, the men of Easy Company universally consider him the best commanding officer they ever had. Subverted Trope in the case of Sobel. While the men of Easy Company attribute their survival during the war to his harsh training methods, he was incompetent in (simulated) combat and had no sympathy for his men. They returned the feeling.
Slightly less evident because he had to manage the entire regiment, but Colonel Robert Sink is more or less stated to be so in the book. David Webster, a member of Easy Company, noted that while the Allied generals would all talk about how their soldiers were eager to go out there and kill Germans, Sink actually knew that the boys hated fighting and tried to make the best of the situation when he could; the soldiers preferred Sink.
This is less evident in the miniseries, where at one point Sink orders a repetition of a night raid because the first raid made him look good to his superiors. Winters, fulfilling the trope, cancels the mission to avoid risking his men's lives.
Babylon 5: Alfred Bester may be a sociopathic Knight Templar and Hunter of His Own Kind, but hurt one of the telepaths under his command and he will tear your mind to shreds and leave you trying to stop the visions by clawing your own eyes out. Corps Is Mother, Corps Is Father...
William Adama certainly gives off this impression, affectionately referred to by most as the "Old Man", and displays paternal affection for his crew in return (at one point, he is shown going through memory exercises to recognize the new recruits by face and name; at another, he sits with a dying female pilot and talks about having a daughter). Which is funny given how crappy his relationship with his actual son can sometimes be.
At least until the events of "The Oath". Damn you Gaeta! Indeed, it is the realization he can no longer trust some of his crew as if they were family that, among other concerns, finally breaks Adama's spirit and drives him to drink and pills.
The scene in "The Farm" where he breaks down and weeps over Boomer's body in the morgue is another particularly good example.
Special mention of Starbuck, who was like that from the pilot. It doesn't hurt that she was in love with and going to marry his son Zack, and therefore was almost his daughter-in-law. Adama takes it very hard on the occasions where it is thought that she was dead.
Adama even goes so far as to call Starbuck his daughter in some of the last episodes.
The time that Admiral Cain was going to have several of Adama's men executed and Adama almost had the Galactica attack the Pegasus over it.
Which is ironic, given that Adama once threatened to murder Cally over something somebody else did ((well, she did do it too, but wasn't the one calling the shots). Essentially, the deck gang went on 'strike' in solidarity with some civilian workers, which Adama technically correctly labelled as mutiny as his crew are not civilians, and since the ring leader (Chief Tyrol) wouldn't call it off, said he'd put ten Cally's up against the wall to safeguard the fleet unless they did. Again, technically, Cally did also commit mutiny, she just didn't lead it
The Bill: Jack Meadows, especially to MickeyWebb. Special mention should go to the episode where, after finding out that Mickey was raped when he was Alone with the Psycho, he tracks him down to his mother's grave and holds him in his arms as he breaks down confessing what happened. When Mickey's rapist escapes prison years later, he tracks Mickey down again to warn him and then offers him his old job back after finding out he's now unemployed. Its also notable that he was originally hard on Mickey, after his ordeal he gives him FAR more leeway then he usually needs.
Code Red has this trope displayed in two ways concerning Battalion Fire Chief Joe Rorchek: Figurative for his whole unit, and literal for his sons who are firefighters under his direct command.
Blue Bloods: Frank Reagan, along with being the most literal example of this trope here, feels responsible for everything that happens to his officers.
Hotch is more than 'can be'. When he and Rossi are gone on a consultation, Morgan outright asks 'Where's Mom and Dad?' There's debate about who's the mom and who's the dad, but Hotch and Rossi have somehow ended up being the parents of their little family.
CSI: Gil Grissom, especially when dealing with the younger members of the team, most visibly Greg, Nick and Warrick (especially right before Warrick gets killed, and afterwards).Jim Brass has also been this at times, and with Grissom now gone, DB Russell is stepping into the role sometimes.
CSI NY: Mac Taylor, especially with Lindsay and Danny at various times, and Flack and Hawkes every now and then. He's pulled Danny back on track multiple times, given both him and Lindsay advice lots of times,comforted sobbing Danny after Danny's brother got beat, was the only thing that kept Flack from committing career suicide and losing himself drinking after Angell's death, let Hawkes use his spare room after he found out Hawkes got swindled and was homeless,and ended up as godfather to Danny and Lindsay's daughter, Lucy. The only reason Stella and Jo don't factor in much is because they're older, more like Team Mom alongside him than the younger ones.
Doctor Who: The Trope Namer for The Brigadier, Sir Alistair Gordon Lethbridge-Stewart. He always led from the front, never asked his men to do anything he was unwilling to do himself, and if you messed with UNIT (including and especially the Doctor), you'd better prepare for a pounding.
Dollhouse: Adelle Dewitt is a mother to her women. She is capable of being a Mama Bear though, if someone harms them.
Farscape: Lieutenant Miklo Braca is introduced to the series as a subordinate of Crais, and after Crais defects and Scorpius seizes control of his Command Carrier, shifts his loyalty to Scorpius. Although for much of season 2 this puts him firmly as an antagonist, by season 3 we come to see that he has become quite the Reasonable Authority Figure as commander. This becomes much clearer in the fourth season, when his respect for his officers and willingness to actually listen to what his subordinates tell him contrasts sharply with the far less forgiving Grayza. When Grayza has her Villainous Breakdown at the end of season four, Braca relieves her of command and not one of the crew present are the least bit inclined to follow Grayza's orders to gun him down.
Flashpoint: Parker is this to Team One. He cares greatly for each team member, can get fiercely protective over them, sometimes refer to them as "children" and at one point even tells Spike that he loves him like a son.
Frontier Circus: In a non-military example, Colonel Thomson took a very paternal interest in all of his performers, and they often came to him to settle problems.
King Renly Baratheon and Queen Daenerys Targaryen are shown to be caring and affable commanders towards even the lowliest soldier in their army.
King Robb Stark's leadership style, as seen in "The Old Gods and the New", where he takes the time to mingle with the rank and file. He explains that he inherited this mentality from his father, Ned. As for Ned, you don't fuck with his bannermen; when confronted by Jaime at the end of "The Wolf and the Lion", he tries to talk his way out of the situation. It was only when his guards were killed did he bring out his sword.
Robb: "He once told me that being a lord is like being a father, except you have thousands of children and you worry about all of them. The farmers plowing the fields are yours to protect. The charwomen scrubbing the floors, yours to protect. The soldiers you order into battle." This is a major alteration from Book!Ned. Jon Snow in A Dance with Dragons remembers Ned telling him and Robb that a Lord shouldn't be too close or fraternize too well otherwise that would complicate The Chains of Commanding, namely that they are the ones commanding those beneath them to fight and die for House Stark and that being a Lord or a leader meant responsibilities, loneliness, distances and no true equals.
While Jon Snow does not start as an authority figure, many of the low-ranking Night's Watch men do look up to him. Averted at the end of Season 5, when he is betrayed and murdered by most of his own men.
For all his flaws, Jaime cares for the soldiers under his command, and tries to offer emotional support to Dickon after he has seen his first true battle. When Daenerys starts raining fire on his army, he is horrified at the sight of his soldiers being burned alive.
Grey's Anatomy: Dr. Bailey is a harsh overlord but is also very defensive of the interns in her charge. On occasion she even seems to see herself as a mother figure, such as after Denny's death.
Grimm: This is played with with Captain Renard, who does appear to genuinely care for the welfare of his men, particularly Nick. Which causes friction to appear with whatever organization he belongs to. On the other hand, he had no problem telling Adalind to drug Hank to get close to Nick. And when Adalind was Brought Down to Normal, he abandoned the former since they were of no use to him anymore.
Heroes: Emile Danko, the Volume Four Big Bad, zigzags this. On the one hand, he chews out Nathan Petrelli when he thinks Petrelli is being insensitive about the loss of those who were killed when Petrelli's family members interfered with their operations, and later gives a Rousing Speech calling for vengeance against a shapeshifter who killed several of his men. On the other hand, it is very heavily implied that he allowed Sylar to kill one of his men so that he could steal his identity and take his place.
Hogan's Heroes: Colonel Hogan's codename is even Papa Bear. He may tease his men on occasion, but he'd go to any lengths to protect them.
Homicide: Life on the Street: Lt. Giardello represents the police version of this trope in many ways; although gruff and aggressive, he'll go to bat for any one of his detectives, and is greatly respected by them in return.
Horatio Hornblower: Captain (eventually Admiral) Sir Edward Pellew in this mini-series. Though he is initially (and loudly) skeptical of Horatio, he soon sees the young officer's enormous potential and comes to regard him as Like a Son to Me. Although he has the greatest affection for Horatio, he feels a deep sense of responsibility for all the men under his command and hates risking life to no purpose, which sometimes puts him at odds with commanders who view common sailors as Red Shirts. At the end of the first series he gives Horatio a speech on The Chains of Commanding emphasizing that he has a duty to his men as much as to King and Country, and one reason he comes down on Buckland in the court-martial of "Retribution" is because Buckland's dithering resulted in needless deaths.
iZombie has the head of the Fillmore Graves Enterprises, Vivian Stoll. She states to consider everyone there her family, knows everyone's names, the children on their educational center all look up and love her, one even running to hug her when they are informed of Wally's death. She was the one that turned the soldier in zombies to save their lives from a bio weapon released on them and she feels personally responsible for them.
Admiral Chegwidden takes this approach to leadership, probably due to his experiences as a Navy SEAL in The Vietnam War.
His "people" are his surrogate family. For all his acting like a "growling old salt" he will go to the mat for any of them. His last act as JAG was to basically demand that the Navy promote Bud despite his career-limiting injury.
M*A*S*H: Both Cols. Blake and Potter to the 4077th M* A* S* H. Radar actually comes out and says this in Blake's case, as his own father died when he was very little. Poor Radar. Even Major Burns, who often had little but disdain for Blake, was noticably upset when the news of his death was announced. Potter may have been the Only Sane Man who was his rank or higher in a series where most such officers tended to be the Colonel Kilgore type.
Mr. Robot has Gideon Goddard, the CEO of Allsafe, the company Elliot works at. He genuinely cares about and listens to all his employees, and even when the company is in serious financial trouble, they're his first priority. He's one of the kindest characters on the show, and even Elliot, who generally doesn't like most people, looks up to him.
Special Agent Leroy Jethro Gibbs, full stop. This probaby has something to do with the horrible death of his wife and daughter stealing his chance to be a literal father. It's most notable with Abby, while Tony seeks his approval in a manner reminiscient of a "Well Done, Son!" Guy (and, in the later seasons, actually gets the 'Well Done'). Ziva, who is the same age as Gibbs' daughter would have been had she lived, has explicitly stated that Gibbs is more of a father to her than her real father, distant Chessmaster Eli David. Especially now that Eli is dead.
This show also likes playing with this sometimes, such as one episode where Gibbs openly calls Ziva his "kid" and implies that he sees the rest of the team in a similar light. Additionally, Abby is often jokingly referred to as "the favorite"...though that's not to say she isn't.
Though Ziva has now become as much of a daughter to Gibbs as Abby. In one episode, when she's considering marrying the man she's been seeing, the whole team (including Gibbs) takes it as given that Gibbs will be the one to walk her down the aisle, and when it falls apart at the end he comforts her just like a parent.
He even claims he's looking for his family after the explosion when he hasn't found them all. He even avenges them by killing the man behind the explosion.
Tom Neville is shown to be quite respected by the soldiers under his command and takes it very personally when a soldier under his command is killed needlessly ("Chained Heat"). Ironically, Neville's own son Jason Neville is assigned to serve under him and despises Neville for his willingness to follow Monroe's orders ("The Stand", "The Song Remains the Same"). Tom Neville turns this into an Exploited Trope by getting Monroe's militia to take his side in a coup, because Neville inspires them whereas Monroe frightens them ("Children of Men", "The Dark Tower").
Miles Matheson is revealed to have been this type of leader when he was the commanding general of the Monroe Militia. This made things more tragic when the situation in the Monroe Republic worsened and he had to sacrifice one of his proteges Alec Penner in order to avoid a war with Texas ("The Night the Lights Went Out in Georgia"). When Miles finally abandoned Monroe (circumstances detailed in "The Dark Tower") and went into hiding as a bartender (shown in "Pilot"), many of his former soldiers felt extremely betrayed by this and grew to hate him instead ("No Quarter", "The Love Boat").
It is stated more explicitly in the licensed novels that Colonel Jack O'Neill takes this view of his team, particularly Daniel, who is younger than he is.
Interestingly, Daniel, having been on the original Abydos mission, was originally the only member of SG-1 to know that O'Neill had been ready to commit suicide because his actual son Charlie shot and killed himself with O'Neill's gun on accident.
General Hammond also behaves like, and is seen as, a father to the rest of the SGC, with SG-1 his favorite sons and daughter.
Weir is simply born by this trope. All her subordinates (except Kavanaugh, of course) are willing to die for her and not out of duty but because that's how much they like her. She was also the only leader of Atlantis who truly didn't mind her subordinates routinely throwing the rulebook out of the airlock because she knew they will win the day. Carter also did this because while she was on SG-1, she also broke the rules frequently. Woolsey, on the other hand, was the polar opposite of Weir. Too bad they can't unfreeze her since she's a security risk, being a replicator and all.
While on the topic of Stargate, Stargate Universe completely averts this trope since it's a three-way power struggle between three factions: Rush (scientists), Young (soldiers) and Wray (civilians). Wray is too weak to do anything on her own and Rush is a straight-out ass so the crew look to Young for leadership and he appreciates it (though we are yet to see the backlash of Rush making Spencer's suicide to look like a murder and framing Young for it; the reason is that Young threw Rush off the ship and lied that Rush got caught in a rockslide).
The trope is later played straight in the episode 'Cloverdale' where, in Scott's imaginary mundane world, Young is literally his father.
Spock risks both his and Kirk's lives to help Captain Pike, who is portrayed as having been this trope before becoming a bit of a vegetable.
Picard in Star Trek: The Next Generation is also a fatherly type (some would say even more than Kirk). He'll go to bat for any of his officers when they're in trouble, and if anyone has disappointed dad perfected, it's this captain.
Sisko from Star Trek: Deep Space Nine, being an actual father is probably the best example, since he knows exactly what to do to pull this off intentionally. He cooks them dinner and takes them to baseball games on the holodeck.
Archer from Star Trek: Enterprise lives up to and discusses this trope with Malcolm, referring to another captain who had a more impersonal attitude. "They're your crew, not your friends." Archer decided that such an attitude wouldn't work on an extended mission light-years from home and cultivates personal relationships with all of his bridge crew, even putting them on First-Name Basis (though they always call him Captain).
President Bartlet, who cares for, stands by and defends his staff even at great political cost, although this is a more metaphorical example, as his "soldiers" are not actual soldiers.
He does at one point refer to Josh as 'my son' - while telling off God for Josh's near death a year earlier...
Although being Commander-in-Chief, he takes his responsibility for the actual soldiers (and sailors, airmen and Marines) very seriously and tries to make sure that they're as safe as can be managed when he sends them into danger.