"Seven years, Dawn. Working with the slayer. Seeing my friends get more and more powerful. A witch. A demon. Hell, I could fit Oz in my shaving kit, but come a full moon, he had a wolfy mojo not to be messed with. Powerful. All of them. And I'm the guy who fixes the windows."
Yuuno Scrya from Magical Girl Lyrical Nanoha is the only Mage in the cast without a magical weapon (he had given it up to the series's titular Action Girl — for whom it was much better suited anyway), so his contribution in battle is largely limited to offering backup, rather than throwing around spectacular offensive spells. He's actually extremely handy in a fight, but he ends up accepting a position in the library of all knowledge where he can pursue his passions as an archeologist/scholar (and give more screentime to the female cast). After that, he participates in only one more fight, and the rest of the time he just researches whatever big nasty or mystery the main cast is dealing with now.
It's possible that Yuuno remains a Non Action Guy because his one demonstrated offensive ability, forcing someone to teleport off the field against their will, offers so many unpleasantpossibilities that neither he nor the series creators want to go there.
Black Butler's Ciel is considered the least physically capable in the entire series, despite being one of the most dangerous in intentions and actions.
Negi Springfield of Mahou Sensei Negima! isn't lacking in courage or combat ability. He is, however, a ten-years-old mage and teacher with 31 gorgeous female students. As such, he still finds himself in situations where one of the more experienced fighters (the ninja, the vampire, the demon-hunting mercenary) among his students ends up bailing him out. Anime-only trope, in the manga he is anything but that...
The resident Non Action Guy of the manga is probably Chamo, who doesn't really do anything combat related other than occasionally acting as The Strategist. Although this is probably because he's an ermine, so his lack of combat ability isn't really his fault.
Rock of Black Lagoon is one of two Non Action Guys in the Lagoon Company (the other is Benny, the resident techie), but Rock has the distinction of being the Non Action Guy thrown right in the middle of most of the violence that Revy and Dutch get into. However, he also stands as a prime example that "non-action" does not automatically equate to "weak" — put a gun to his head, and he'll not only keep it but quite possibly throw it back in your face. This fearlessness, combined with his ability to network, have made him recognized as one of Roanapur's most dangerous figures, despite his never even touching a gun.
Yuichi Tate from Mai-HiME usually gets into situations where he finds himself over his head. It isn't until the final episode that he finds his... er, manliness.
Less apparent in the manga, where he's still largely useless but at least tries, and his presence is in fact necessary for Mai and Natsuki to access their full powers.
He tries in the anime, he just ends up realising quite quickly that there's very little a normal person can do to help in those sorts of situations and decides to take himself out of the game to take care of Shiho, whom he thinks got hurt because he left her alone while he ran off to try to play hero. Also, while the method of his involvement in the finale is arguably a bit stereotypically manly, he wasn't trying to play hero there. He just decided he cared enough about Mai to be willing to put himself on the line to help her out a little. Anime Tate only gets to be cool when he's not trying to be.
In Mirai Nikki, Yukiteru spends the vast majority of his time running crying and screaming from the people determined to kill him. He occasionally fights back when cornered, but more often than not he's saved by the wrath of his psychotic stalker-girlfriend.
He gets increasingly more action-oriented during the second season, culminating in episode 19, when he single-handedly destroys a (albeit somewhat pathetic) Guze no Tomogarra with five bodies by flambéing three of them, snapping one's neck, and impaling the last on his BFS, and becoming a nice asset to the team until he falls to The Dark Side and becomes the Big Bad in season three.
Sports manga examples: Taro Misaki from Captain Tsubasa is an excellent soccer player on his own right, but he's so often plagued by injuries (in the first tournament he's injured by Hyuga, in the World Youth Cup he's hit by a bus and breaks his leg and/or emotional issues (he's shown as VERY reliant on Tsubasa in one of the movies, to the point of seriously lacking leadership skills and having a serious crisis for that) that he often Can't Catch Up with others.
Another one is Syuuichirou Oishi, the gentle Seigaku sub-captain from The Prince of Tennis. Putting other people's well-being before his own actually causes more than a bit of trouble, both physical (as he gets his arm injured right before the Hyotuei matches and such an injury has repercusions later) and mental (not only he has quite the breakdown in the Jyousei arc of the anime, but he later gives up his spot in the regulars to Tezuka (manga) or Echizen (anime), thinking he's a burden when he's not). This makes him look less skilled and strong than he really is, and as a result he's unfairly ignored in fandom and only featured in fanwork regarding his partner, Eiji Kikumaru even when Eiji has him in such high regards that, after he loses Oishi, he swears to not have * any* other doubles partner than him.
In Mnemosyne, Maeno plays a role much like Black Lagoon's Rock, mostly playing a helping hand in investigations, but avoiding the combat, for good reasons.
Tsukune from Rosario + Vampire was initially the weakest student at Youkai academy, due to being human. He was heavily reliant on Inner Moka's strength, as well as that of his other friends. About halfway through the first season, he gained the power to fight on his own, but he doesn't become a full-time combatant until the second season. In the anime, none of that happens, so he remains the Non-Action Guy in both seasons.
Aoyama, Ryou and Keiichiro from Tokyo Mew Mew — although the constant switching around of one of the boys in question was used to set up a few Red Herrings as to the identity of Ao no Kishi.
With his first re-appearance after the time-skip in the latest manga chapter, this is hopefully a thing in the past. He now seems capable of taking down yoma singlehandedly, and all fans are now praying to the Character Development Gods that he has taken multiple levels in badass.
Oh yes, he has. Has he ever. His latest exploits include holding off two of the titular Claymores by himself (they were still rookies, and they were holding back, but still), and facing down about a dozen of the Organization's Mooks and winning, without even taking as much as a scratch.
In Kaleido Star there's the stage manager Kenneth "Ken" Robbins, who has a heart condition and can't join the troupe of acrobats and artists. To make up for it he becomes Sora, Anna and Mia's Lancer when it comes to training, strategies and planning.
In One Piece, Usopp is generally a coward that runs from all signs of danger, and he's a lot weaker then everyone in the main cast (he isquite durable...but his crewmates are even moreso). The few times he gets a serious fight, he usually wins by nifty use of a wide array of gadgets.
Eventually he becomes quite a bit stronger and less of a coward, but he still relies on his tricks and gadgets.
Lelouch Lamperouge from Code Geass is an odd case: He's a Magnificent Bastard and genius Chess Master, but so horribly unfit you'd be excused for thinking he's anorexic. He has been easily outrun by girls wearing mascot costumes, fancy dresses with petticoats and high heels. He's routinely curbstombed in mecha battle. It's even lampshaded symbolically with the show's chess theme, where Lelouch plays the part of the king, simultaneously the most important piece and the slowest moving. Yet despite all this, he's anything but cowardly or harmless: On his own he has managed to easily infiltrate and take control of several aerial battleships, and from the very first episode he killed large groups of hostile soldiers with ease. Even without his Geass he is shown to be very competent with a gun and can score headshots if his targets aren't endowed with Charles Atlas Superpower, and in the second episode he doesn't even flinch when Villetta is firing her knightmare-mounted machine gun at him. Essentially, half-Non Action Guy, half-Badass.
Rivalz Cardemonde also counts, as he's present in all the Ashford scenes, but never does anything relevant, although as a genuine Ordinary High School Student (as opposed to the multiple characters who only pretended to be), he may just never have any opportunities to show off.
Kyon in Haruhi Suzumiya (who is also the Unfazed Everyman), at least when compared to Koizumi and especially Yuki. This is justified by his being the only member of the Brigade without any sort of supernatural ability (Wild Mass Guessing aside). Interestingly, in spite of this, he's still able to get his stuff done, even if it takes him three tries to clear a level.
Roderich/Austria from Axis Powers Hetalia. He was "created" by Vash/Switzerland to be a fighter, but it failed spectacularly and he ended up as a pint-sized James Bondage. He didn't get a lot better as he grew up into one of the two Team Dads of the series, but he had the good sense of mostly staying as Mission Control and leaving the fights to the Ninja Maid Elizaveta/Hungary, whom he later married.
Feliciano/North Italy. His whole character seems to be based on this trope.
Chiba Mamoru/Tuxedo Kamen from Sailor Moon is totally this in the anime. He says a few words to bolster Sailor Moon's spirits, throws a rose, and wanders off. He has to be saved from death/possession (season one), brainwashing/his own stupidity (season two), villain-induced illness (season four), and death (season five), not to mention many smaller instances. Except for providing The Power of Love a few times and a pivotal future cast member, he's kind of useless in battle. Possibly a case of Can't Catch Up, since the Sailors get regular upgrades while he... uh, doesn't.
ONLY in the anime, though. In the manga he had an actual attack and awesome mind powers — including healing, a psychic connection to his loved ones, and the ability to feel the earth's pain — and beat up bad guys more often. He was much more Bad Ass as a villain, as well. Still a prime target for the Worf Effect, though...
Nijima of Kenichi: The Mightiest Disciple is the only member of the Shinpaku alliance (well, other than that guy who carries the flag) who has absolutely no fighting skill.
Gau from Nabari No Ou, despite technically being a ninja. His only function seems to be to hold Raikou's sword, stand at the sidelines, shout "Raikou-san!!", and to be attacked by the enemy, effectively turning Raikou's battles into escort missions.
Monster's Johan Liebert has three ways to kill people: shoot, poison, and drive them to suicide. Though this is probably less "useless in a fight" than "so terrifyingly good at manipulating people that he doesn't need to fight."
Cruz from Needless is literally the single most harmless guy in the series as he does not have any powers and always end up saved by third parties.
Mikiya Kokuto from Kara no Kyoukai could be considered pretty badass by normal standards but there is only so much that a normal can do. He does have his moments at times when he felt it is necessary but for the most part, he sticks to investigation and information gathering, which he is very good at, and leaves all the fighting to his Action GirlLove Interest, who is also very good at what she does.
Considering how dangerous investigations can be in his line of work, he gets a decent amount of action trying to get away from danger.
Yuuen from Wild Rock, to the point his father decides he will be more useful pretending to be a girl to get food rather than hunting for it.
Teruharu Kousukegawa from Change 123 is a particularly standout example, given that he nevertheless has a nasty habit of trying to interpose himself between danger and his friends, who are usually fifteen to twenty times stronger than he is.
Guin Sard Lineford of ∀ Gundam is the ruler of Inglessa and a competent strategist who is one of the most active forces in the show. But the only time he picks up a weapon himself is either to take it off someone else or to fake a Hostage Situation.
Several in Mobile Suit Gundam SEED and Mobile Suit Gundam SEED Destiny, all of them useful or competent in other fields. Sai Argyle is leader of the Archangel's Bridge Bunnies, and is far more valuable when it comes to running the ship than he ever would be in a fight. Patrick Zala and later Gilbert Durandal serve as ZAFT's leaders and as such don't have to get their hands dirty (although given Patrick's past as a general it's entirely possible that he'd do just fine in a fight; the key here is that we never see him actually in one). And Muruta Azrael and Lord Djibril? As the leaders of the anti-Coordinator terrorist group Blue Cosmos, they don't need to be fighters in order to be dangerous. Azrael in particular combines this trope with Smug Snake, Axe Crazy, Bad Boss, and Nuke 'em.
Mizuki from Kamisama Kiss. He is far stronger than any normal human and has quite a bit of magical power but so far he hasn't shown any fighting skill whatsoever and has a real laid back personality.
The Tick'ssidekick, Arthur, is a pudgy accountant in a moth-suit that he barely knows how to work. His battle cry is "Not in the face! Not in the face!"
Marvel Comics had a villain who fit this trope: Sidewinder, especially after he'd founded the Serpent Society. He acted as the group's Mission Control, setting up deals, deciding who would go on which assignments, etc. He still managed to give the superhero community fits, because he'd also habitually teleport his teammates out of jail. A perk which is the biggest reason for villains to join the Serpent Society.
In Legion Of Super-Heroes, Dyrk Magz loses his magnetic powers in a fight with Mordu. However, he can't bring himself to stay in civilian life and comes back to work as Mission Control. He served a crucial role in a battle with the Fatal Five (see the Quotes page).
Fone Bone from Bone — all the threats he faces in The Valley are so much larger than him that he invariably has to run away or get rescued. He's no coward, but his courage involves giving moral support and good advice to to resident Action Girl Thorn, rather than busting heads himself.
Ringo in With Strings Attached. Lacking any defensive or reliable movement magic, he has to be toted around and protected by the others. He's hardly useless, though, even if he does have a moment or two where he feels like The Load.
Actually, in a sense all four are Non-Action Guys, since they do not want to be involved in adventure and have zero interest in combat.
Mr Ping of Kung Fu Panda. He has no kung fu skills whatsoever, and devotes almost all his time to manning his noodle store.
The character WALL-E certainly qualifies, especially in comparison to trigger-happy EVE. A Determinator who saves humanity from its own indolence, sure, but non-action regardless.
Film - Live-Action
Rick Moranis' character Louis in the movie Ghostbusters fills this role for the Ghostbuster team. Even when he tries to be a Ghostbuster himself he is a goof.
Rick Moranis' character Billy Fish in Streets of Fire, on the other hand, at least has bowling-ball-sized testicles to make up for the fact that in action situations he's utterly useless.
Abe Sapien is mostly the geeky backup to the burly Hellboy in the first movie. When he faces Mr. Wink in The Golden Army, he proves to be quite acrobatic, but still barely escapes with his life until Hellboy shows up to save the day.
Every single Racer in Speed Racer is a capable hand-to-hand combatant. Except for Sparky, who's... not.
Lenny Nero in Strange Days is a classic example of this as a protagonist! He spends much of the action in the movie getting saved by Mace. This is made a little strange when it's revealed that he's a former cop.
"Sir Robin the Not-Quite-So-Brave-as-Sir-Lancelot, who had nearly fought the Dragon of Angnor, who had nearly stood up to the vicious Chicken of Bristol, and who had personally wet himself at the Battle of Badon Hill" from Monty Python and the Holy Grail.
In Blade II, Blade's new sidekick Scud is a noncombatant. When confronted by Reapers, Scud retreats into his van and nearly has a heart attack. In contrast, Whistler ambushes a den of vampires with a gatling gun in the first film and guns down a few SWAT guys in the third.
Topher Grace's character in Predators is introduced this way. In a team of professional and criminal badasses, he is an unassuming doctor with no particular combat or survival skills. The badasses spend most of the movie protecting him or at least trying to keep him from getting them all killed, until the end, when he reveals his true nature as a murderous psychopath.
Frodo Baggins in "Lord of the Rings" is more or less this. Whilst Hobbits generally are Non Action Guys, Merry, Pip, and Sam can and do throw themselves into the action when the 'taters are down. Frodo tends to whimper and swoon when faced with combat against anyone but Gollum.
Erek King from Animorphs is an ageless, nearly-indestructible android perfectly capable of being a One-Man Army but is bound by his programming which prevents him from harming other living things. This is probably for the best - the one time he does fight, it's so brutal it leaves the resident Blood Knightin tears.
Ron Weasley... of all the characters in the Harry Potter series, he always seems to be the one so friggin' out of his league it's not even funny.
Neville Longbottom is an even better example of this, particularly with him "becoming" a man in the final book when the "worthier" dominant males (Harry and Ron) have vacated the position.
Rincewind is one main character in Discworld who prefers running away from... everything, really.
A more straight example is Nijel the Destroyer, son of Harebut the Provision Merchant. He wants to become a barbarian hero (by reading books), but has some... problems. He promptly fall in love with Conina, who's the daughter of Cohen the Barbarian and has inherited her mother's looks and her father's urge to kill. She really wants to become a hairdresser.
Moist von Lipwig is another protagonist example; he's not at all comfortable with fighting, preferring trickery and disguise instead.
Every single Hobbit almost without exceptions. Of course Hobbits have Hidden Depths and the book can be mildly Anvilicious about that sort of thing, though fortunately the author's skill keeps it in control.
Artemis is far better suited to orchestrating everything from behind Butler and letting his more athletic companions do the dirty work, but as often as not circumstance forces him to at least try to do something physical anyway. It seems like he resolves anew to start getting fit at least once a book, but it never quite happens.
This is subverted by Artemis's Split Personality Orion whose shooting skills (something that Artemis doesn't have) disabled a controlled Holly.
Miles Vorkosigan: With brittle bones and stunted growth due to a pre-natal poison attack on his parents, it is often pointed out to Miles that his proper place is behind the action, giving directions to the more physically capable. This usually happens while Miles is in the hospital, recovering from injuries he sustained while being in the middle of the action.
And Commodore Baz Jesek, while Miles's nominal second-in-command for several books, starts the series as a deserter. Honour regained, he's never seen in a combat setting again, being more gifted at engineering and organising and supporting the more action-y types - such as his wife.
Elend Venture of Mistborn is this in the first two books, perhaps most powerfully illustrated when he rushes off, armed only with a duelling cane to rescue his girlfried, Vin. She winds up saving him (though the cynical Vin was very touched that he actually cared enough about her to risk his own life). Elend takes level in Badass in the third book, and though he never eclipses Vin he establishes himself as more solidly on her level.
Spook from the same series is pretty tough by normal standards, having grown up on some very nasty streets, but he's only a Tineye (translation, he has Super Senses but is otherwise baseline human) in a setting where most of the really important people are superhuman badasses and/or have said badasses working for them. Consequently, he knows better than to get mixed up in the action until he too takes a level in badass in the third book.
Sazed subverts this. He insists that he's no a warrior but is perfectly capable of holding his own against for more powerful characters such as Marsh, whom he comes within seconds of defeating during their only fight.
To the general populace (in-universe, not to most readers) of Tamora Pierce’s Tortall Universe, George Cooper is this. He's a just an ex-commoner who married Alanna, Champion of the Gods, first Lady Knight, heiress to an ancient dukedom and all around badass. Of course George does have his claims to fame—like being the former King of Thieves and current Spymaster for the nation.
Waldo Butters, M.E., in The Dresden Files. He is, as Thomas insists on pointing out, kind of a coward, and when the baddies wind up targeting him in Dead Beat, spends most of the book hiding from them. However, this isthe Dresdenverse, so he eventually winds up saving Harry by attacking Cassius with his teeth. He also gets non-action awesome cred for helping with the Dinosaur Incident.
Simon, in Mortal Instruments, is the only main character that is 100% a mundane and is depicted as totally normal and needs rescuing from a hotel crammed with vampires. However, this is ended when he kills a Greater Demon, and then is turned into a vampire in the second book.
Mind you, he does need saving again a couple of times even after that, namely from dying of blood loss in Valentine's ship, and then from being killed by the normal Brooklyn vampires for being a Daylighter
Jason Richter from Dale Brown books starts as this. Although he's a Major, he's really an engineer who hasn't touched a gun since Officer Cadet School, unlike Pat McLanahan who can handle himself on the ground even before receiving further combat training and becoming a Tin Man. At one point, he even visibly winces at the prospect of having to kill. He gets better, partly due to having El CID. Some Sky Masters personnel also joined the company without being part of the military first and thus are ill-prepared to actually use the equipment in a live-fire situation against hostiles actively trying to kill them.
Karal in the Mage Storms trilogy of the Heralds of Valdemar. He's a priest in training, is a certified Nice Guy, has no magical or psychic powers (except for one, which is completely passive), and has absolutely no interested in heroing. It doesn't stop him from playing a pivotal role in saving the world.
The Hunger Games: Peeta Mellark is the series Guile Hero and plays Non Action Guy to his Action Girl love interest. This is especially prominent when he's compared with her other love interest. He is mentioned being good with a knife and a wrestler, but it's more of an Informed Attribute since we never actually see him fight and all his badass moments involve playing the crowd. This actually turns out to be a good thing as while Katniss has the skills to surivive in the arena, its only through his charisma that they're able to manipulate the audience and so stay alive. Ironically if she'd been in there with her other love interest they probably would have died.
It's the default in the world of A Brother's Price. Because men are so rare, they are kept sheltered and are almost universally more tenderhearted than the women who run the world. Jerin is seen as weird because unlike most he was taught to shoot and ride a horse, which serves him well when he is abducted, but he quickly falls off said horse into the protective arms of a much tougher love interest, and when he actually uses said gun it is textbook Bleed 'em and Weep.
Adrian Monk. As an ex-cop, he's fully capable of holding his own in physical combat, but his complicated network of phobias and neuroses make him freak out at the thought of physical contact, placing him here.
Xander of Buffy the Vampire Slayer. He gained in combat ability throughout the series, but was still a second-line fighter at best by the end, taking on the Mission Control role in the "Season 8" comics. Even so, he's another example where lack of combat ability is compensated by extreme testicular fortitude; his more powerful friends often worry about his near-suicidal charges against superpowered opponents.
Lorne, from Angel. While the rest of the team fights evil, Lorne's major skill is singing. It's not so much that Lorne is incapable of combat as that he hates it.
Daniel Jackson from Stargate SG-1. Gradually became more suited for action.
Also, most of the male scientists on Stargate Atlantis qualify. Of the three main male science-oriented characters — Carson, Zalenka, and McKay — McKay is the only one who regularly has to go off base, and he is all but worthless in a fight. (A good example is the time he has to be explicitly instructed to open fire on an advancing Wraith, and then again to reload once he's run out of bullets!) Of course, as many missions involve the rest of the team protecting him while he performs some variety of technobabble, so he is far from useless. Carson and Zalenka are even less action-oriented due to how rarely they leave Atlantis. (Though Carson's ATA gene allows him to cause quite a bit of damage with drones, he is very nervous at the idea of using them and has a VERY difficult time controlling them. It doesn't help that, as a doctor and a truly gentle man, he is about as much of a pacifist as he could be without packing his bags in protest.)
While Zelenka doesn't see much action and clearly dislikes it, his age and nationality suggest that he probably has some background in the military. For all that most people probably wouldn't look to him in a fight, he drops a marine in "Tabula Rasa" and manages to avoid many more of them for most of the episode when forced to fall back on instinct.
In the first season of the new Doctor Who, Mickey Smith is explicitly set up as The Guy Who Doesn't Have What It Takes, in contrast to Action Girl Rose Tyler. In the second season, to justify his continued inclusion in events, it turns out that he does Have What It Takes after all.
The Doctor himself qualifies for the trope as well, as with the exception of his third and sixth incarnations he runs away from the Monster of the Week as often as he runs toward it.
Original series companion Harry Sullivan was conceived as an Action Guy in case an actor too old to handle action was cast as the Fourth Doctor. But when they cast Tom Baker as the Fourth, Harry immediately became this instead and was quietly dropped in Baker's second season.
Rory Williams was very much this before he became The Last Centurion. He would much rather become a small town doctor than fighting aliens.
In Dark Angel, Action Girl Max had Logan Cale (Michael Weatherly) as her Non-Action Guy; in a wheelchair, partly because it would help prevent him from being seen as The Chick in comparison to Max's superhuman strength.
Ianto Jones in Torchwood has absolutely no desire to leave Mission Control, and reckons the rest of the team are adrenaline junkies. But he gets action from the hero, if that counts...
Ianto seems to be getting in on the action (in multiple senses of the word) more in the second season. And by the third, he spends more time by Jack's side than anyone else. Although that doesn't end well.
Owen even mentions this at one point when he's sidelined, more or less implying that this is what Ianto actually wanted... Of course, this could just be Owen being Owen.
Ironically, the reverse often happens in more recent PR. Most notable is Cam of Ninja Storm, although the Super Sentai version combined with Cam's wardrobe made it an easy enough guess.
Mention must be made of Ziggy in RPM, as he starts out a Non Action Guy and pretty much remains one throughout the season, even after he becomes Ranger Green. He's competent in a fight, but only competent, and still a bit of a coward.
Det. Pembleton from Homicide: Life on the Street is a rare example of "empowered" Non Action Guy; Pembleton is constantly portrayed as an ace detective and as one of the most prominent and charismatic characters of the show, and yet he detests weapons and is a lousy shot.
Which is about exactly the same as Lieutenant Columbo.
Will from Alias. He's not an agent like most of the men on the show. He manages to get himself in trouble trying to be tough and Sydney has to rescue him. Even though he starts to work for the CIA and makes some results, he's still only a paperpusher.
The Lone Gunmen - all three of them (four, if you count Jimmy). None of them were anything close to action guys. What they did have was a copious amount of brainpower and bullshit.
Jonathan Creek, arguably. If there's buildings to be broken into or criminals to be confronted, expect Maddie/Carla/Joey to do it. Jonathan hangs back, watching what's going on and deducing the truth from what happens.
Except that one time where Jonathan disarmed a gun-wielding multiple murderer by throwing, of all things, a playing card at his hand.
Topher in Dollhouse once gets beaten up by a one-armed Non Action Girl. That pretty much sums up his physical prowess.
DR Spencer Reid. He's the only member who failed all physical FBI phisical exams, but because he's a genius with 4 PH Ds, Photographic Memory, and reads 20 000 words a minute. There's a reason that any time a character is kidnapped or in danger its Reid, the writers even named those kind of episodes as "Reid In Peril" episodes.
In the season 2 episode Revelations he manages to kill Tobias Hankel after being drugged repeatedly, tortured for two days, being forced to dig his own grave, and actually dying.
Wash from Firefly knows that his job is limited to flying the ship and providing needed levity and snark, and leaves the fighting to his amazon-like wife Zoe. His acceptance of their non-standard relationship (aside from a brief bout of unfounded jealousy in "War Stories") results in them having arguably the happiest and most stable relationship in the whole show. Unfortunately, that's probably why he was killed in the movie.
Subverted with Shepard Book. At first glance he seems a kindly, elderly preacher, with elements of the Wide-Eyed Idealist and at best, seems to be Badass Pacifist. Our first clue is him working out with Jayne. Our second is his surprisingly large knowledge of the military arts. Our third is him shooting a man in the kneecap from the hip holding a large rifle with one hand.
Andrew Ridgeley from Wham! is the canonical example in British music journalism. To his credit, he actually broke up Wham! when he realised just how ridiculously far ahead of him George Michael was. That said, he still released an utterly superfluous solo album.
WWE wrestler Stevie Richards once spent a considerable length of time not wrestling, and instead accompanying borderline-psychotic woman wrestler Victoria to the ring for her matches and acting like a submissive, lovestruck little puppy. He also wore pink tights. Maybe he just got sick of being a jobber....
Back in the mid 90s, Triple H Hunter Hearst Helmsley was perfectly happy to hide behind his female bodybuilder bodyguard Chyna. Although he wasn't purely non-action, back then he did completely rely on her.
A particularly domineering heel will often have a non-wrestling male attendant whose job is to help them cheat and to get beaten up by the face so that the heel can use the distraction to flee the arena. Examples of this type of character include Daivari for Muhammad Hassan (although Daivari did have some wrestling skills himself), Ranjin Singh for The Great Khali (before their Heel Face Turn), and Ricardo Rodriguez for Alberto Del Rio. Sometimes, though, the attendant will be even more physically intimidating than the wrestler he serves (Ezekiel Jackson or Tyson Tomko, for example), with such "enforcer" types obviously being more likely to end up wrestling on their own and throwing off the "Non Action" status.
Allen Ridgeley from the Xenosaga games is a textbook example. Despite accompanying the hero party everywhere, he is only called upon to fight once as a guest party member during Episode 3 and is laughably bad; during the final climax, he managed to combine heroism with trope loyalty by pulling a Gandhi when confronted by the heroine's now-antagonistic ex-boyfriend, saving HER from More than Mind Control, redeeming the ex-boyfriend, and then machine-gunning a Gnosis to death. He took a level in Bad-Ass, after being useless for three games!.
Otacon of the Metal Gear series is about as Non-Action as possible, a Bunny-Ears Lawyer of an engineer with nerd glasses thick enough to rival Gordon Freeman, but that doesn't stop him from being vital to Snake's success in all three of his appearances.
Zexion of Organization XIII fame in the Kingdom Hearts series prefers scheming over combat. Even when he finally gets to fight in RE:Chain of Memories and Kingdom Hearts II Final Mix, he doesn't do much (He can't attack unless he absorbs Riku's power in the former game, and in the latter his only move is to trap Sora, Donald, and Goofy into his Book dimension, from which he can attack them completely indirectly.)
Demyx from the same Organization in the same series likes to pass himself off as one of these, running away from enemies, claiming he really doesn't know how to fight very well, and using a sitar as a weapon. He'slying.Bigtime.
In 358/2 Days, Demyx's claims tend more towards laziness than incapability, probably because he's more likely to stay not-Duskified if he keeps them thinking that he IS good for something, and it's just a matter of getting him to do it.
He's also apparently the greatest scout in the organization.
Thomas of Suikoden III has the same Star as the previous two names' badass heroes, but if you're expecting Kung-Fu Badass... you're sorely mistaken. He's rather meek in personality and is quite terrible in combat. Fitting since he's not a fighter, but a businessman. However, he makes up for it for being The Determinator.
If you bother to level him up to be on par with the other main characters, he can be competent in a fight, but most players don't bother since he starts all the way down at level 1 and even when built up he'll still only be an average fighter.
At one point in Breath of Fire III, you have to train a bookworm named Beyd to become an Action Guy in order to get into a lighthouse. (He has authorization, but has to prove he's stronger than his romantic rival to justify going.) If trained properly, he wins his fight... and ends up so badly battered that he just gives you the go-ahead to enter while he recuperates. (On the plus side, he gets the girl.)
Most of the player characters in the Silent Hill series are not someone you expect to be able to kill gods with whatever weapons they find lying around, though as the plot progresses it's clear that the ordeal causes them to Take a Level in Badass. (How well the level takes depends on which of the Multiple Endings you get.)
Notable exceptions to this are Travis, a trucker whose Dark and Troubled Past is fairly obvious even before The Reveal, and Alex, whose combat abilities are explained as having come back from the military ( though even THAT comes into question, and is somewhat foreshadowed throughout the plot).
Knox, from Vampire: The Masquerade - Bloodlines is a ghoul, and very, very aware that he cannot reasonably be expected to survive a fight against a vampire. Which is why he cons you into doing it for him.
Henpecked Hou from Jade Empire was once a competent and respected Drunken Master... until he got tricked into marrying a woman who disapproved of drinking and fighting, and could back up her words. If you have him accompany you, he won't fight enemies, but instead throws wine bottles that allows you to use Drunken Fighting style. On the other hand, he has enough courage to follow you into any sort of danger... as long as you're there to protect him.
Heavy Rain's Ethan Mars. Despite that, he is willing to save his son, Shaun.
Roman Bellic from Grand Theft Auto IV is the protagonist's overweight, optimistic and somewhat cowardly cousin. Niko kill people for a living, Roman runs a cab depot. He puts up with an incredible amount of abuse through the game, being beaten up, having his home and business burned down, shot, kidnapped, stuffed into a trunk, and more, mostly as mission fodder for the player. At the end of the game he may or may not be killed at his wedding. Still, he takes it with reasonable good cheer, and having his cousin around does make him rich.
In Golden Sun: The Lost Age, the scholar Kraden is the fifth member of protagonist Felix's party for 99% of the game, yet never takes part in any of the fighting. Weirdly enough, appears to make him immune to monsters, since he's never actually endangered by the constant monster attacks. In the sequel Golden Sun Dark Dawn he again takes on this role.
Makai Kingdom: Lord Zetta is very much a non-combatant, since he is trapped in the form of a book and cannot even hold a weapon, and has to rely on his servants to fight for him. When Alex, God of Destruction, challenges him to a one-on-one fight, defeat seems inevitable... until Salome, Zetta's former apprentice and lover, swoops in and tears Alex a new one.
Joker from Mass Effect. Not a playable character (bar a short sequence, mostly involving running/limping away, in the second game of the series) his brittle bone disease makes him worry about breaking bones whilst DANCING let alone fighting. Of course he can make the Normandy do things that no-one else thinks it should be able to do.
Then inverted in Mass Effect 2 during the final scenes, where he wields an assault rifle holding off Collectors so that Shepard can escape onto the Normandy.
Ib has Garry, who begins his appearance by lying down on the ground and painfully (nearly) dying. You get to save him. Especially evident when you contrast him with Ib (a 9-year-old girl), who is the one to do the saving, and solve pretty much everything. However, Garry does get a Crowning Moment of Awesome and save Ib if you complete a certain event a certain way. If not, Ib has to save him instead.
Tedd of El Goonish Shive is like this. He acts as Mission Control in the only combat arc he is involved in, and he can be rather cowardly at times. Then again, he is a scientist-type character surrounded by shapeshifters and supernatural martial artists, so it is to be expected.
Dr. Shelton and Dr. Kerzach from Darwin's Soldiers start the first RP as this. Dr. Kerzach and Dr. Shelton do end up taking a few levels in badass but they are still nowhere as badass as the other characters. Dr. Bailey from the third RP plays this straight.
Ron Stoppable of Kim Possible fame starts out as this, though he gradually becomes better (and even saves the day in the very last battle of the Grand Finale). Most of the time, he only demonstrates his competence when Kim isn't around, so Overshadowed by Awesome may also be in play.
Jérémie Belpois of Code Lyoko, who operates Mission Control while the others fight all the battles. Yet he is also the team leader, since when your enemy is an evil computer AI, the most crucial member of your team is the computer genius.
In Lilo & Stitch, in all its incarnations so far, Pleakley is a Non Action Guy whenever the action shows up.
Rattrap was forcibly turned into one in Beast Machines, much to his annoyance. However, he was as resourceful as ever, and when the need arose was usually able to exploit the environment to defeat his enemies.
Fry from Futurama. While he certainly has his moments (only person who can defeat the Brainspawn?), in most stand-up fights he's cowering behind Leela.
Mad Mod of Teen Titans qualifies for this. In his first appearance, he is an old man who attacks the Titans with a holographic version of his young self who uses hypnotics and moving objects. Then, in his second appearance, it's hypnotics and robots. Oh, in the same episode, he is back to his younger self thanks to absorbing Robin's youth.
Averted in the Justice League animated series as Martian Manhunter is usually the "inacton guy" on the satellite directing things and he just happens to have pretty much the same powers as Superman, plus psychic abilities, plus he's a shape-shifter.
While he does have his moments, Spike almost never fights, is rarely actively involved in fixing problems the protagonists have and usually contributes to the group through managing small scale tasks for them and doing their menial work, fitting this trope quite readily.