The Major from Hellsing. For an Omnicidal Maniac enamoured of war and carnage, he noticeably lacks any combat involvement and limits himself to inspirational speeches.
Hilariously, he can't even shoot a disobedient soldier standing right in front of him, despite emptying a clip of ammo at him. Eventually, he just has his more loyal Mooks do the killing for him.
Spandam from One Piece is the leader of the Cipher Pol 9, an elite group of government assassins. He's also physically weaker than a single common fodder soldier.
He actually does have a Cool Sword: The Elephant Sword. The problem is that he can hardly use it properly. When he unleashes it on Franky, Franky convinces the Elephant to squish SPANDAM
Nagi dai Artai in Mai-Otome, albeit largely because males can't become Otomes.
Gato in the first arc of Naruto, which ended up being his undoing after he tried to dispose of Zabuza for failing to defeat Kakashi, only for Zabuza to return the favor by killing Gato himself. After that, every other Big Bad in the series has fully embodied Authority Equals Asskicking.
Sakyo of Yu Yu Hakusho is head of the antagonists in the Dark Tournament Saga, even if Toguro overshadows him in plot importance. He also knows he can't fight, despite being the fifth member of Team Toguro, so he says that the outcome of Toguro's match will decide the outcome of his, thus enabling whoever wins it to win the tournament.
Though it happens offscreen, it's made clear that he has numerous innocent people "disappeared" because they saw something inconvenient, and further it's implied that he did that solely to annoy Section 9 who would find out anyway. And that's not even accounting the attempted nuking of millions of people.
Kyubey from Puella Magi Madoka Magica. He never actively bring the girls into harm, he simply gave the girl their wishes and let them fight witches as magical girls as payment. There are only two reasons to consider him a villain at all: he doesn't value individual human life at all (and doesn't even understand the idea), and he is directly or indirectly responsible for everything bad that happens in the series. The reason it's all arguable is that he's doing it to prevent universal destruction due to entropy. A more "traditional" Big Bad is Walpurgisnacht, but that is more of a force of nature than a true enemy.
Neither Degwin Zabi or his son, Gihren were up to much physical action in the original Mobile Suit Gundam. As the political (and military in Gihren's case) rulers of Zeon they didn't need to be.
In the anime Gihren ends up getting his brains blown out by his sister Kycilia after he kills his father with aWave Motion Gun. Interestingly, in Yoshiyuki Tomino's original 52-episode plan for the series, Amuro actually gets to confront Gihren in person, but even then all he does is rant at Amuro and die in a hail of gunfire.
Chancellor Wong in G Gundam is the bad guy in the second act- he's super manipulative (he even has literal chess-pieces in the shape of the Gundams), is the De-Facto leader of everything and holds authority over MasterAsia... however, he hardly stands up from his floaty chair, only sets up fights for Domon, and has an L-Level sweet tooth. Suffice to say, he's almost vaporized by collateral damage—which was the direct result of his own manipulations—and when he actually gets in a Gundam (unwillingly) he lasts all of two minutes. And most of those two minutes are spent talking.
The king in Chess. It's barely superior to a simple pawn, and spends as much time as possible hiding and fleeing (especially since it usually can't attack another piece without moving into check first).
Sin City baddies tend to be this trope. The Roarks, Ava Lord, Wallenquist, and the Colonel never get their hands dirty and are likely incapable of doing so. Instead, they send dirty cops, mooks, hitmen, and assassins to do their jobs.
In most forms of media, The Joker is this - he's generally portrayed as scrawny, and occasionally it will only take one punch from Batman to bring him down. He makes up for it by being a Magnificent Bastard.
In the pages of Iron Man and The Avengers, we have seen guys like the Roxxon Oil heads, Justin Hammer, and the leaders of the Maggia who were corrupt business men or mafia bosses who could not go up against the heroes one-on-one and often employed super villains. Obidiah Stane and Count Neferia also started off this way but both men either gained powers later or eventually wore a suit if Power Armor.
Darth Vader, of all people ended up this way in the Marvel Star Wars comics. The reasoning behind this was that Lucas Arts did not want to have Vader and Luke fighting too often, lest it conflicted with the movies, which the comics were supposed to coincide with.
Dieter von Cunth in MacGruber, for all his fearsome reputation, just stands there and gets his ass kicked when the finale comes.
Sauron from The Lord of the Rings film series is a partial case. He does come out, and he DOES do some major damage in the prologue against the Last Alliance. But he never comes out to play again during the main story arc; in the film explicitly because his form is just an eye on his tower.
Rex Lewis/The Doctor/Cobra Commander in G.I. Joe: The Rise of Cobra. Slightly subverted. While he does leaves the dirty work to his Vipers and McCullen, he does use his tools in wanting to torture Duke. Which makes sense since Rex blames Duke for his apparent death.
In Animorphs, the Council of Thirteen may count as Non-Action Bigger Bads, as they're political leaders and their hosts are apparently just normal Hork-Bajir and Taxxons (though a few have unknown hosts). They could take a normal human in a fight, sure, but they probably wouldn't stand up to the Animorphs. Their morph-capable servant, Visser Three, is the real Big Bad.
Subverted with Visser One. You wouldn't think a middle-aged housewife could be very formidable in a fight, even if she is controlled by the leader of the initial invasion of Earth. You would be wrong.
Grand Admiral Thrawn from The Thrawn Trilogy. He's actually implied to be at least a decent fighter, and is described as being powerfully built, but he has no interest in engaging in combat himself- it's strategy and trickery that hold his interest, not brawling. The Thrawn Trilogy Sourcebook gives him ridiculously high stats, but then again it's made so that fans can roleplay through the events of the trilogy, and they might be able to force a physical confrontation.
Explicitly averted in one of his later (but chronologically earlier) appearances. One of Thrawn's intricate plans includes a requirement for an elite bounty hunter's involvement. The bounty hunter is the linchpin of the plan, and would have to be given more information than such an inherently mercenary individual should be trusted with. Thus, Thrawn simply puts on a suit of Mandalorian armor and assumes the role himself. Sharpshooting included.
The Big Bad for the first six books of Galaxy of Fear is a Shi'ido named Borborygmus Gog. While the series' other Shi'ido, Hoole, takes several different forms in order to fight various menaces, Gog prefers to use his talents for impersonation and trickery. His menace comes from his projects and schemes, and while he menaces people with a blaster a couple times and once detonates an Explosive Leash in a creation's skull, he never actually fights anyone himself.
Lord Straff Venture in the second Mistborn book- he's a thoroughly evil man, but is middle-aged, out of shape, and a Tineye (meaning that he has magical abilities, but they involve Super Senses rather than anything physical). As such, he prefers to work through his army and his Ax CrazyDragon and illegitimate son Zane.
Lord de Worde in The Truth doesn't hit people. He hires people to do that.
A Song of Ice and Fire provokes endless debate among fans as to who the Big Bad is, or if indeed such a Crapsack World even has a single person who would qualify. However, all of the possible candidates fall into this trope, as they are all politicians and manipulators who do not do any fighting themselves.
The First Evil in Buffy the Vampire Slayer who, having no physical form, must resort to Mind Rape as well as The Dragon and its Elite Mooks. It does not want to be this trope and attaining a physical form is implied to be its endgame (since it is Made of Evil, the more evil it can make the world the closer to fulfilling this ambition it gets). On the flipside, it is completely invincible and As Long as There Is Evil it will always exist, so its a pretty high-functioning example of this trope.
Dr. Wily in The Protomen's albums. It's lampshaded in Act I.
King Cepheus and Lady Vega in the first two Mega Man Star Force games tend to rely on their ultimate weapons, Quirky Miniboss Squads, and minions to do the fighting for them. In both games, the final boss isn't the villain, it's the device they planned to use to take over/destroy (delete as applicable) the world.
Sofia Lamb from Bio Shock 2. Andrew Ryan of the first game as well, until you deal with him and Fontaine takes over the show.
Bob Page from Deus Ex. Although he's in the process of becoming a god, at that particular stage in the process he's so vulnerable that effectively all you do is turn off his life support.
Henry Leland in Alpha Protocol. He can be the final boss, but the fight is a joke and its made clear that this is just an act of desperation.Sergei Surkov is also one.
In the arcade version of The Combatribes, the main heroes spent the last two stages chasing after a man in a suit who fits the image of a stereotypical crime boss. When the crime boss is cornered in the final stage, he is betrayed and killed by his female bodyguard Martha Splatterhead, who proceeds to fight the player in her boss' place.
Caesar of Fallout New Vegas does not fight in the game unless you decide to assault his fort, preferring to let his Dragon Lanius take command of the military campaign. It's justified in that he's an aging man with a brain tumor and doesn't put up much of a fight by himself, though statistically he is equivalent to an Elite Mook with nonexistent armor since he wears ceremonial robes and is surrounded by Praetorian Guards.
In the Old World Blues DLC, there's Dr. Mobius. While he spends the entire DLC siccing his Robo-Scorpions on you in as maniacal a manner as possible, when you actually meet him he turns out to be a heavily senile and grandfatherly old brain who can barely remember half of what he says. Most of his more maniacal rants are due to him taking Psycho. You can fight him, but he's hardly a match for you. Similarly, The Think Tank at the end are equally pitiful in combat, though it's made clear early-on that without their pacification field there's nothing stopping you from curb-stomping them.
Major General Nikita Dragovich from Call of Duty: Black Ops. The best he can muster against Mason and Hudson when he confronts them directly at the end of the game is to try and shoot the former with his sidearm, before being easily beaten up and choked to death.
The same can be said of Imran Zakhaev from the original Modern Warfare. Without his Ultranationalist armies to protect him, he's just an angry old dude with one arm. The only reason he manages to kill Gaz and most of Soap's other squadmates is because they previously had a tanker truck explode in their faces. The moment Soap gets hold of a gun, he's done for.
After spending the second game in an uneasy alliance with Shepard, the Illusive Man becomes this in Mass Effect 3, with Kai Leng acting as The Heavy. It's kind of like they split the role Saren had in the first game into two people - Shepard and the Illusive Man constantly try to talk the other around to their way of thinking, while Leng is an exclusively physical threat who ends up on the wrong end of Shepard's omni-blade.
Originally, the creators intended for the players to fight a reaperized version of The Illusive Man as the final boss. However, they felt that since TIM was meant to be a villain whose intelligence was his greatest weapon it would undercut the character for him to become a Giant Space Flea from Nowhere.
Dr. Breen in Half-Life 2. The final battle consists of sabotaging his teleporter before he can run away (nuking you in the process), while he taunts you.
Dr. Neo Cortex of the Crash Bandicoot series, he's a super genius and at least arms himself with a deadly laser gun, but he's also a weedy midget with a head almost bigger than his stick-like body. Granted Rule of Funny applies on occasion, in Crash Twinsanity he actually brawls with Crash toe to toe.
The alien brain in X-COM does absolutely nothing but sit in its underground base, waiting for someone to shoot it.
Jack Denham in Syndicate (2012). He tries to shut down your CHIP, but when that fails he doesn't raise a single weapon.
Victor Branco in Max Payne 3. The one time he tries to pull a gun on Max, he gets disarmed quickly and only The Dragon saves him. The "boss fight" with him is just blowing out his private jet from under him.