Mogi from Death Note: the quietGentle Giant who stays with the Japanese task force through thick and thin, doing whatever is needed in an efficient manner, even when it means playing WAY against type and acting like a hyperactive kissass manager to spoiled, self-centered Elegant Gothic Lolita Misa Amane. Along the way he draws praise from figures as different as Director Yagami, L and Near for his dedication, skill in compiling reports, and refusal to accidentally give away information with an ill-timed word.
Hayate himself of Hayate the Combat Butler is a rare case of the main character being this. Since he is a butler and a good portion of the cast are rich but socially naive girls and an assortment of wacky and highly unreliable people this makes sense. When he isn't being focused on, he can even be seen doing...well darn near anything really. He steadily acquires more girls to support and helps them with their problems as well as handling minor chores and such that often goes unnoticed (though the girls are pretty observant and very grateful for his help).
Maria was this toward Hayate and Nagi in the beginning as the reliable older figure (only by a year)who came in to sort out a mess in a few panels whenever messes got too big due to Hayate's abysmal luck. This has been somewhat phased out as Hayate has gotten more accustomed to the job and Maria's own quirks were dialed up a bit for humor.
Hinagiku becomes this to Hayate over the course of the series. They start out as friends, but eventually Hayate starts going to Hinagiku for all of his problems, especially those he didn't want one of the other girls to know about and typically finds out about the messes he didn't want her to know about either. It helps that she's more proactive about it and prone to worrying about him when he's acting off and thus tries to find out the problem on her own to help the poor guy out.
Arata of Saki Achiga-hen. Her status as such is why Harue chose her as the Club President for Achiga's mahjong team, in spite of Yuu being the only third-year and Shizu taking the initiative to revive the club.
In The Boys, the titular group is a CIA organization that keeps tabs on and confronts the often wild and sociopathic "Superheroes" of that world. It seems that Mother's Milk is often Overshadowed Bythe Crazy Awesome that is the damn weird Frenchman, the Ax-Crazy Female, the Magnificent Bastard Butcher, or even The Woobie newcomer Hughie, but Butcher frequently says that he can't run the outfit without MM and for good reason. Hughie is the Naďve Newcomer to a hopeless degree, Butcher is often blinded by his hatreds and need for revenge, and both The Frenchman and The Female are far too crazy or off in their own world for Intelligence or detective work, so when it comes to taking care of the day to day functions, MM has to do it or it won't get done and the group will collapse or become ineffective.
Snake Eyes in G.I. Joe. If he is needed somewhere or a task needs to be completed, he will be there and get it done without doubt.
Practically all of Scott's friends need to have some degree of this in Scott Pilgrim because Scott himself is notoriously flighty and unreliable, but the best example is probably Kim Pine, his long time best friend, high school ex, and arguably his biggest help in getting his head screwed on straight.
Alfred from every Batman comic ever is the perfect example of this. He is always there when Bruce needs him. He'll set a bone, make a cup of tea, or yell at Bruce until he agrees to sleep.
Fatal Instinct. Ned Ravine's secretary Laura Lincolnberry is a perfect example of this trope. She takes care of minor matters for him, helps him pick out his outfits and keeps her head on straight.
Arthur from Inception. He's not the Master of Disguise, or The Charmer, or The Profiler, or The Smart Guy with the new sedative that makes the impossible possible, or the architect who creates dream worlds from nothing. He's criticized in one breath for "Having no imagination", while in the next he's praised for being the best at what he does: being The Comically Serious guy who always watches your back and makes sure you come out of things okay.
R2D2 in Star Wars. Co-piloting, repairing, picking locks, saving heroes from a Death Trap, smuggling weapons or valuable data, etc, etc.
Elizabeth Pennykettle from The Last Dragon Chronicles is almost a personification of this trope. If anyone has a problem, she's guaranteed to be the one who fixes it for them. She's also a giver of motherly advice and lends an ear in times of trouble. See also: Team Mom and Deadpan Snarker
General Carvaille is this to Robert Epine, mixed with Poisonous Friend, in Reflections of Eterna, to the point where Robert muses in the later books whether Carvaille is the real regent instead of him.
Dr. Watson in Sherlock Holmes. No matter what Holmes asks of him, he will perform above and beyond the call of duty, running errands, writing detailed reports, dropping his work to help with a case, and engaging in such tireless efforts as rushing from London to Paris within the span of a day when he hears Holmes has fallen ill, to spending several weeks acting as a threatened client's bodyguard, to risking his life by remaining by Holmes's side while the latter experiments on himself by filling the room with poisonous fumes, all without ever backing out or making a half-assed effort, and only failing when Holmes makes him do tasks that require a level of genius he does not possess. Holmes even comments on this trait several times.
It is really very good of you to come, Watson. It makes a considerable difference to me, having someone with me on whom I can thoroughly rely.
Live Action TV
In Smallville, Chloe Sullivan is always there whenever Clark needs her, and this often extends to his other associates.
Lennier in Babylon 5. As Delenn's aide it's his job, but he goes far above and beyond the call of duty in too many ways to count.
Willow:(sarcastically) Old Reliable, yeah, that's really a sexy nickname. Xander: She means you're like a geyser of fun that goes off at regular intervals. Willow: That's Old Faithful. Xander: Isn't that the dog that the guy had to shoot... Willow: That's Old Yeller. Buffy: Xander, I beg you not to help me.
Later on in the episode Willow refers to herself as "reliable dog geyser person."
Teresa Lisbon (The Mentalist) always has Patrick Jane's back: Jane calls her his 'moderating influence'. Grace Van Pelt from the same series often goes unnoticed and unappreciated for the long hours she spends hunting down files and information for the other characters.
From Scrubs: Carla, the steadfast, cool-headed, keen-eyed, ever-competent, always-on-top-of-things head nurse, is the most reliable employee at Sacred Heart. Even outside of her job, she's usually the person everyone runs to with their problems.
Stiles on Teen Wolf. He is the Hypercompetent Sidekick to both Scott and Derek, as well as being strongly committed to protecting virtually everybody, even enemies such as Ethan.
In the episode "Motel California", Stiles enters a big puddle of gasoline, to stop Scott, who is drugged and holding a lit flare, from committing a fiery suicide even though odds were good that he would be burned to death if he failed to get the flare away from the super-strong Scott.
Ianto resents being this in the first series of Torchwood.
Guinevere in Merlin, who whether a servant or a queen, is always diligently hard at work throughout the entire series. An example of her competence: it takes Arthur two consecutive seasons to realize that there are traitors at work in Camelot, and both of them escape his justice. It takes Guinevere two episodes to find one, and then she manages to use the traitor to lay a trap to successfully neutralize the real threat.
Merlin may also count, most prominently toward Arthur. Even if nobody besides Gaius knows it, he routinely manages to find out traitors, defeat dangerous magical threats and save Arthur/somebody/Camelot nearly every episode while always being there for Arthur.
Friends: Monica, whose apartment is the refuge of the whole gang and she's consistently the go-to-girl for solving their problems.
Hawkeye, Trapper and Henry Blake can always rely on Radar O'Reilly in M*A*S*H not only to hear choppers before anyone else, but also to play a part in the zany scheme of the week. It's even Lampshaded in one episode where Radar is heartbroken after receiving a Dear John letter and messes up the order forms. And again spoken in the episode 'Dear Dad'.
Hawkeye: (voice over) I'm not quite sure what Henry would do without Radar....
The protagonist is virtually every open-world RPG that includes quests. You will run around completing all sorts of tasks for everyone, from getting a book on the table next to them to slaying a demon that has cursed their family for generations.
A rare case of such character in a main role: Eddie Riggs from Brütal Legend, who is a roadie who helps his friends make history but willingly sticks to the backstage throughout the game.
There's also the APC unit in Advance Wars. It can't actually attack, but it can do a lot of useful things, like carry your infantry, act as bait (particularly in the first game) and resupply other units.
Link acts as the reliable one in several Zelda games, but especially The Legend of Zelda: Skyward Sword, where his reliability allows him to help the people of the sky and retrieve Gratitude Crystals from them in order to help the demon Batreaux become human.
Link takes this trope Up to Eleven. It's been stated that the Hero is reborn each time Ganondorf returns to threaten the world, which means Link is such a reliable One-Man Army, dungeon crawler, and general Evil Killer, that his spirit reincarnates specifically to battle evil whenever it grows too powerful. If that ain't reliable, nothing is.
There is one exception to this rule: when Ganondorf broke free from the Sacret Realm between Ocarina of Time and Wind Waker. Turns out his arrival was only delayed, but because of this the godesses had to flood Hyrule.
And then a day came when a fell wind began to blow across the kingdom, and the great evil once again crept forth from the depths of the earth. The people believed that the hero of time would come again to save them, but the hero did not appear...
Sarnel of Drowtales is well aware that Ariel, as heir to one of the most powerful clans, The Val'Sarghress, in their Underground City of Chel'el'Sussoloth, will need reliable people beside her, who can help her survive and lead, so he fully plans to be this for her. His own grandfather is this for their clan's leader Quain'tana and is in fact the very reason their clan is so powerful.
Durkon from The Order of the Stick. Frequently cited by the fandom as the least interesting or developed character, (due in part to Our Dwarves Are All the Same) he's nevertheless a major part of the glue that holds the Order together, and is usually the one that its members come to for advice, help in trials of leadership, conscience, or against self-doubt. And every time he's not with the Order and they face a major obstacle, the Order starts to fall apart.
Redcloak is this for the bad guys. He even lampshades it in one strip.
Redcloak: It's all fun and games for them, but I'm the one who has to make the magical, lightning powered trains run on time.
Burter and Jeice seem to consider each other to be this in Dragon Ball Abridged. Leaving aside their boss, the other members of their team are a psychopathic Blood Knight who always thinks that he's in a wrestling match, and the Butt Monkey whose ability to stop time is the only useful thing about him. So when Burter needs someone by his side in a fight, or Jeice needs a favor, they call each other.
The Head Scholar of The Questport Chronicles is ostensibly just a librarian, but the Lord of the Supreme Council delegates a large amount of responsibility to her.
In Off The Page And Into Life, it doesn't matter whether she's never met you, you don't want any help, or even if she doesn't particularly like you. Gail Rubens will do whatever she can to help you. This is the reason Mr. Valjean asks her to ease the other teenagers into the news of Colleen dying—because he knows she's mature, empathetic and responsible enough to actually be able to do it. While this puts some stress on Gail, she comes through, and even considers becoming a hospital chaplain because of the experience.
Applejack in My Little Pony: Friendship Is Magic, who is the most cool-headed, hardworking, reliable pony in the show, and actually has her own episode where it's showcased how she does too much for other ponies without thinking of herself. Occasionally it comes back to bite her, as she's so dedicated to helping out that she tends to be a bit stubborn about it. In "Applebuck Season", the entire conflict was that Applejack refused to stop trying to help around town despite the fact that her farm work left her so sleep deprived that her "help" did more bad than good.
Spike as well. He's always there mostly for Twilight Sparkle but also for anyone else who needs him, and knowing they appreciate it is good enough reward. It's hinted in Owls Well That Ends Well and later confirmed in The Crystal Empire that his greatest fear is not being this to his friends.
In Teenage Mutant Ninja Turtles (2003), Donatello gets less attention than Mikey, Raph, and Leo. But meanwhile, he's been finding old junk and appliances and fixing them up so his family can live comfortably underground. Without him, they might not even have lights or hot water, let alone television. When their second lair is destroyed, he takes it the hardest because of all the work he put in.
On The Looney Tunes Show, Daffy Duck pontificated about every character's role in the group. And this was a parody of such tropes, partly because he would change his mind within the same conversation (is Porky Pigthe buffoon or The Reliable One?) And most of these lists included calling at least one character "the reliable one," showing awareness of this trope.