Feng Shui, the "Action Movie Roleplaying Game", divides foes into two categories: Mooks and Named Villains. Villains with a name are built from the same archetypes as player characters and get all the benefits the players do — Wound Points, deadly skills and feats, the works. Mooks get the ability to attack poorly, and are out of the fight when someone hits them with an attack whose Outcome after subtracting the mook's attack skill from the action result is five or more, and the player can choose whether or not they're either knocked out or dead. Unarmed fighters usually prefer knocking mooks out, though those with deadlier weapons will often go for killshots.
One of the schticks available to Feng Shui players is a Gun Schtick called 'Carnival of Carnage.' It has four levels, the first two of which reduce a gunslinger's shot (action point) cost when attacking mooks, and the second two of which reduce the Outcome needed to take them down.
Exalted has a similar mechanic, with "Extras" whose sole purpose is to be mowed down by the players. They have three health levels instead of seven, take greater wound penalties, and serve no purpose except to slow down the players (unless they're on the players' side, in which case they serve as cannon fodder/footsoldiers).
Usually, they have a hard time doing even that.
Yeah, the real purpose of Extras (who also show up in Scion) is to show just how much more awesome the PCs (and their villainous counterparts) are than the average mortal.
This rule has appeared in other White Wolf games as well, such as some old World of Darkness titles.
Mutants & Masterminds have 'minion' rules that make them easier for the heroes to drop in large numbers quickly. The rules make them very weak, including allowing the hero to "take 10" on the attack roll, making missing them unlikely, and the feat "Takedown Attack" allows you to drop unlimited Minions as long as they are within melee reach and each one falls in 1 hit.
Dungeons & Dragons in its 4th edition has "minions", a category of monster that explicitly serves purely to fill out the ranks in encounters. They have exactly one hit point each (though they never take damage from missed attacks, even those that would normally do half damage otherwise — you do actually have to hit a minion to knock it out of the fight), attacks that deal fairly low fixed damage, and simply much less detail in general than their fully fleshed out counterparts because they're meant to go down easily and aren't worth the effort; XP-wise and for encounter planning purposes, a single regular monster is considered the equivalent of four of them. (It's worth noting that some monsters come in both regular and minion flavor, depending on the level of party expected to encounter them and general role.) In earlier editions, the traditional "mook" niche would often be filled by humanoid monsters with only one or two hit dice, which mid- to high-level characters could pretty easily kill in large numbers without worrying overmuch about getting seriously hurt in turn.
While they have no specific mechanics for it, the rulebooks and scenarios for Warhammer Fantasy Roleplay and Dark Heresy usually contain 'minion' characters with no names, subpar stats (they will usually never stand up to a Player Character overall, and their best scores are average by PC standards) and have less than 10 wounds, which allows all but the most unfortunate attacks to instantly splatter them. They also die the moment they take a Critical Hit, where player characters and named foes (usually) take at least one or two penalties called 'critical damage' before croaking, giving the minions an on-average shorter lifetime of one to two rounds.
Unknown Armies provides GMs with generic Goon stats; though in earlier stages of the game (given its intentionally weak combat skills) they can be quite dangerous when armed.
Justified for Cartoon Action Hour, which is a kiss-up to 1980s cartoons. They call them "Goons", which are just an unarmed, armed weapon or ranged weapon check which is either up to the Player or the Game Master.
7th Sea divides antagonists into three categories: Villains, Henchmen, and Brutes. Brutes are transparently Mooks: their purposes are to buff a villain or henchman, and to provide the heroes with easy victories (players are encouraged to come up with creative ways to knock down two or more brutes at a time). Since in Seventh Sea, it is assumed that no character is killed unless someone specifically states that they're doing so, Moral Dissonance is sidestepped.
In Savage Worlds (somewhat similar to other examples) any character with some degree of plot importance (even if it's just as a Boss Battle or similar) is a Wild Card: they get Wound points, their own bennies (used to re-roll dice and soak damage), and generally better gear and Edges (feats). While all player characters are Wild Cards by default, enemy characters generally aren't.
Represented by the "Cannon Fodder" rule in GURPS. Minor NPCs under its purview always fail attempts to dodge and are taken out automatically by any amount of damage.
Anyone of Minor importance in Hong Kong Action Theatre is a mook. They can mow down characters of no importance, and take down a Moderate importance character, but against Major and Extreme importance characters, they tend to die in droves, particularly since explosions, which do not affect Major and Extreme importance characters, can take them out instantly.
Fantasy Craft has two kinds of characters, Standard and Special. Standard characters are the normal enemies, but they can be given the quality "mook" which makes them instantly fail their save against damage and die.
In general, having explicit mook rules of some sort or other has become a pretty common feature of modern tabletop RPGs since Feng Shui (which may well have been the first). The idea proved just that popular.