It should be noted that nearly any game with a combat basis will have you face against some form generic minions.
Slimes are some of the most famous! Let's see... first enemy you face, starting monster in the Mons spinoffs, give 1 EXP and 1 Gold, come in many different variants including Metal Slime and King Mook, only have about 10HP ever...
GOOMBAS! As well as Koopa Troopas, Spinies, Lakitus, Hammer Bros., Magikoopas, and the rest of the Koopa Troop.
The Pokémon games absolutely love the latter category of mook. Almost without exception throughout the series, the actual leaders of any criminal organization are a genuine threat... but the legions upon legions of grunt-level members are a bunch of nameless goofballs who are played almost entirely for laughs and are minor obstacles at best.
It helps that they seem to just blindly recruit people off the streets. The Mooks of Team Galactic don't even know what they're being terrorists over.
To make things worse, since Generation II, all trainers are named. However, those organizations' grunts are never named. The sole exception to this are the Cipher Peons; it'd be almost impossible to distinguish one from another otherwise.
In fact, the games expect you to defeat every single grunt because they give good EXP. The bosses at the end are at the level where you'd need to train so you can beat them. This is especially true in the first few games and their remakes.
Evil Genius takes the further step of explicitly telling you that Construction Workers are expendable and can be used as cannon fodder; they're still necessary, though, as they're the only ones who can build new rooms.
EarthBound features a minor enemy species actually named Mook found in large quantities in certain dungeons.
Senior Mooks, on the other hand, have powerful PSI that can drop Paula in one hit.
Not as conveniently named, but Foppy and Fobby are perhaps the embodiment of this trope: they are nondescript little blobs with feet, they are completely ineffectual in battle, they give massive experience compared to other enemies in the same areas, and it's unusual to face them any less than three at a time.
But if they were left alone for several turns, they could concentrate again and start casting powerful PSI powers, which might make them Elite Mooks, or even a lethal Underground Monkey
Foppies and Fobbies aren't the only ones like this. Others include the Slugs and Mr. Molecules.
Sadly, MOTHER 3 has no alien Mooks. Instead it has Pigmasks, most of which are laughably dumb or cowardly.
The Waddle Dees from the Kirby games are not only completely ineffectual, they barely even have faces. Although they are adorable little guys but get disposed.
Mooks are the primary resource in most games in the Dynasty Warriors series. They're technically capable of hurting or even killing your character, and they can get between you and the more important foes you're trying to take out, but their primary purpose is to die by the hundreds and provide a bountiful harvest of experience points, arcade-style power ups, morale and, above all, entertainment.
The beat 'em up genre, consisting of titles such as Final Fight, Streets of Rage and Golden Axe, could be seen as the forerunner to more recent series like Dynasty Warriors. The threat posed by even the most lowly mook in 16-bit era beat 'em ups is more significant, but not by much.
Ace Attorney Investigations has "good" mooks, in the 99 policemen who follow Shi-Long Lang around. They tend to block your path or drag Gumshoe away when he's trying to be helpful to Edgeworth, but they're on the side of the angels and at the end of the game one of them even pulls off a Big Damn Heroes moment.
Used in City of Villains, where one of the early enemy types you encounter are a branch of the local mafia called "The Mooks". Like almost all enemy types in the game, they're an endless supply of easy beatings and experience points, with only the named bosses being particularly dangerous.
The identical nature of mooks was lampshaded in Serious Sam: The Second Encounter, where Sam asks of one, "Didn't I kick your ass two rooms back?"
Deus Ex pits the player largely against humans wielding the exact same weapons the player can use. They also use the same model as the player for taking damage and dying.
Until the mid game, these mooks pose a serious threat as individuals, and more than three at a time is reason enough to look for a maintenance tunnel or sniper's nest.
The mook status is lampshaded in one mission where a mother begs you not to shoot at her son, who is one of the mooks outside. Her description is composed of elements hidden by the uniform, and chances are good you had to take him out just to get in and talk to the woman.
Deus Ex goes beyond lampshading and into bona fidedeconstruction. Many of the game's faceless mooks have multiple lines of unique dialogue, and mooks constantly have conversations which Anviliciously drive home the point that they are real human beings who probably don't deserve to be gunned down en masse just because you don't feel up to sneaking past them or incapacitating them non-lethally.
Except that they are trained soldiers and police with, for the most part, orders to kill you on sight.
Except that apart from MJ12 goons they were misinformed that you are a terrorist.
In Metal Gear Solid 3, the enemy soldiers (GRU or KGB or Spetsnaz, or some combination thereof) are so disposable (at least on the lower difficulty settings), at one point a bunch of them die to killer bees, while their leader (a plot-important character) simply kills all the bees that come near him. With his guns. By twirling them in the air. Snake, meanwhile, has to jump to probable death, to avoid certain death. Needless to say, he survives as well.
The TimeSplitters series has evil henchmen in employment of the evil Khallos...EVIL, however, he does provide them with communal dressing rooms and rubber miniskirts for female members.
The short Vietcong campaign in Vietcong 2 is something of a subversion of this. You spend a few levels playing as a young Vietcong soldier, then the campaign's ending shows your character as one of the countless nameless mooks your American character mowed down in the main American campaign.
The running enemy grunts in the original Contra for the NES. As a reward, the quantity of these grunts increases each time you complete the game.
One of the biggest and most egregious abusers is the Grand Theft Auto series from III onward, especially San Andreas and IV. Most of these time these mooks just magically appear after a cutscene with no real explanation why they're there other than an out-of-hand implication that they're working for an antagonist that was in said cutscene. There are even entire missions where the whole point of the mission is to kill a specific collection of mooks.
Most levels in Banjo-Tooie have their own variant of the basic enemy that runs after you swinging its fists or some sort of blunt instrument: Ugger in Isle o' Hags (and a few other areas); Moggie in Mayahem Temple; Billy Bob in Glitter Gulch Mine; Jippo Jim in Witchyworld; Keelhaul in Jolly Roger's Lagoon; Guvnor in Grunty Industries; Biggyfoot in the icy side of Hailfire Peaks; Flatso in Cloud Cuckooland.
A large part of Batman: Arkham Asylum is spent either beating Joker's mooks into pulp, or slowly and silently taking them out from behind.
Every Ratchet & Clank game typically has one group of reoccurring organic mooks (the Blarg, Thugs-4-Less, Tyhrranoids, Drophyds, Agorians) and robotic ones (Drek's robots, Megacorp security, ninja bots, DZ Strikers, space pirates, Nefarious Troopers).
World of Warcraft (and typically any MMORPG): "Greetings, Darkvarriorz. We need your help; go kill 15 [Mooks with a sword], 12 [Mooks with a bow] and 25 [Mooks with an axe] from the Defias Brotherhood and come back to see me".
The Bilgewater Goblins, introduced in Cataclysm, have a race of ogre-sized labourers... named Mooks.
A Guilty Gear spinnoff game features the Mook Squad: Hundreds of generic guys with Only Six Faces, occasionally using Palette Swap to look more varied. Three of them can be unlocked but besides walking jumping, throwing some punched and kicks and sometimes a special attack or two (and sometimes not even that), they are next to useless. And you can't even assign them to the AI.
In Fur Fighters the mooks come in a couple of different shapes and sizes but it's generally three different types of Bear, a Peacock, an alligator, an armadillio, a Guns Akimbo Dingo, and a cow with different clothes depending on the level you're in, with polar bears standing in for the Elite Mooks.
In MadWorld, every enemy EVER ENCOUNTERED (aside from bosses and the big mooks you get once or twice per level, like Big Bull and Yee Fung) is a mook.
Any non-Boss Heartless in Kingdom Hearts. After you find the Keyhole in Traverse Town, the Heartless in Traverse Town serve two purposes; acquiring munny and Level Grinding.
Averted in Dishonored. There are many city guards called "The Watch", and they are after protagonists. But its because he was framed and they have no idea he is innocent. They are definitely not faceless, and they have many quotes indicating they are normal people just like everyone else. Game also rewards player for not killing them.
Valkyria Chronicles puts a lot of effort into giving Mooks a bit of dignity; the enemy soldiers all look the same, but some of them have specific names and are notably more bad ass than average and are worth remembering, your militia squad is colorful and full of personality, and there's a scene in one chapter devoted to the death of a single faceless enemy Mook who dies in the protagonists' arms, forcing them to realize that the enemy is human too. This doesn't extend to all the ally Mooks, who get slaughtered en masse and no one gives half a damn.
Every single soldier on the battlefield (around 600) except you and the one or two bosses in Sengoku Basara exist only for you to cut down in style with your flashy skills. 99% of them don't even try to either attack you or defend themselves. However they do provide some quite amusing background dialogue.
The Legend of Zelda series can be a little unclear about which enemies are Mooks. It's typically accepted that Moblins, Bokoblins, and any permutations thereof work for Ganon/Ganondorf, and Stalfos are a safe bet, but it's anyone's guess as to whether Octoroks or Keese do or they're just mindless animals attacking Link.