Don't you just want to pat the cute little guy on the head (with your feet)?
"Day One: I'm called up for the draft and enlisted as a Troopa A member of the ground assault in the army of King Koopa My assignment is a grassy hill beside a massive cleft They told me when the plumber comes to 'just keep moving left' The bastard finally showed up, so I marched without delay But he just jumped right over me, continued on his way! At no point in my orders did they mention moving right! So I stepped right off the edge, filled with paralytic spite." — Yahtzee Croshaw, "Cabin Fever"
A type of Video Game Character. This is that one enemy that will always be encountered in the first level (and usually, but not always, as the very first enemy in the game), has a simple movement pattern, and is reassuringly easy to beat. They are the meekest and mildest of Mooks, and are the very first entries in the Sorting Algorithm of Evil. Stomping or blasting one of these guys for the first time marks the moment where the person holding the controller really starts playing the game. Basically they're here to help you learn how to attack, and to spoon-feed you your first few EXP.
In old-school RPGs, this will usually have a Slime or Slime-like monster, although Goblins are not unheard of.
Is usually victim to becoming an Underground Monkey. Oftentimes their lowly cannon-fodder status is subverted by making Underground Monkey versions be the rarest (and sometimes toughest) enemies in the game - see Metal Slime. Sometimes they are dangerous because of the sheer number of them. If being attacked by one takes one hitpoint, then being met by 100poses a problem. If any monsters are recruitable, expect this to be the Joke Character, maybe the Lethal Joke Character.
Often serves as practice fodder leading up to the Warmup Boss. If they become numerous enough, they can also become Mascot Mooks. A Goomba-type enemy is often a Waddling Head. Compare Com Mons, Mooks. Contrast Demonic Spiders.
Watch out, because they might turn out to be the Not-So-Harmless Villain towards the end of the game. (see also Magikarp Power)
Note: the term "goombah" is still a live piece of offensive slang in the Northeast of the U.S.; use with caution around Italians stronger or meaner than you are (unless they are gamers, but especially if they're plumbers), or if you just plain don't want to be a jerk.
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Octoroks fulfill this function in many Zelda games. Chu Chus seem to have joined them, as of late.
Critters in Cave Story. They do get the Underground Monkey treatment and become progressively more dangerous the farther you get in the game.
Red ninjas in the Ninja Senki. The other ninja variations are all quite dangerous however. The toads also count once you get used to their jumps.
When you first enter the Guidance Gate in La-Mulana, the skeleton is the first type of enemy that you encounter. Skeletons, like bats, occur throughout the ruins; they do become tougher in later levels. They take more than one hit to destroy without a certain item you can't obtain until fairly late in the game.
The Combine "civil protection" in Half-Life 2. Sure, they come in groups and some of them have SMGs, but they're cannon fodder compared to Overwatch soldiers and the Overwatch soldier know it. All of them go down in two headshots from the weakest gun in the game, they have no concept of cover and fields of fire (meaning it's very easy to score those two headshots), will alwaysshoot from the hip, and have a bad habit of Fast Ropinginto the immediate path of a speeding vehicle.
Headcrab Zombies. Their claws and bites hurt quite a bit, but they're very, very slow. They're also completely braindead (purposefully so, in a series widely praised for its Artificial Brilliance) allowing for plenty of funny moments. The developers love putting large, heavy props and environmental traps for the player to kill them with.
Headcrabs are the best example: they're small, die from two bullets or one good crowbar whack, do pathetic damage, and are some of the first dangerous things you encounter in the game. They're also seriously terrifying.
Subverted in Unreal. The first enemies you come across are the Brutes, tough hulking monstrosities with weapons that deal splash damage. Later in the game their inability to move quickly and dodge your fire make them die fairly quickly, but when you encounter them the first time you're armed with nothing but two peashooters and you have very little armor, and it's quite possible to get killed by them. The second enemy you encounter (the tentacle plant), however, definitely counts, as you can dodge its shots indefinitely and it goes down if you sneeze at it.
In Left 4 Dead the common infected are scattered everywhere.
BioShock the regular Splicers, who are armed with either melee or ranged weapons.
Wizard Of Wor has every stage begin with Burwors, which don't move too fast and can't turn invisible.
World of Warcraft doesn't have rats as enemies, although kobolds are somewhat rat-like... but they only serve as The Goomba in the human starting zone, where they share the dubious honor with wolves and bandits. Some other starting zone enemies are a subversion as the essentially same type can be encountered again much later, such as the forest trolls in the blood elf zones that also inhabit the Zul'Aman raid instance.
City of Villains have the Snakes, which are naga-like humanoids. By level 10, you'll be thoroughly sick of fighting them, and won't see them again... until the late 40s, where one set of missions sends you back to the starting zone to fight Elder Snakes and their goddess, who are proportionately much tougher.
City of Heroes has the Hellions and Skulls- two street gangs, one a group of Satanists, the other a death cult. Both are explicitly at the bottom of the heap in both games.
But both games have the weakest enemies of all in the tutorials; heroes fight hooligans hopped up on what barely counts as Psycho Serum ( but which turns out to be plot related) while villains practice their punches on prisoners and guards in the Zig.
In Guild Wars, river skales fill this role in Prophecies, and mantids do the same in Factions.
Ace Online/Air Rivals starts you out by hunting mostly harmless giant bugs. It isn't until you bump into the I-Gear Early Types near the end of the starting mission set that a fairly competent opponent appears.
Circle MUD had the 'beastly fido', which almost all of it's inheritors kept.
Gnolls are the very first enemy you fight in the prologue of Vindictus. Your first mission, however, pits you against Wood Men, who attack much like the gnolls.
Another Nexon game, Maplestory has the Mushroom and its variations, and (to a lesser extent) Snails and Slimes.
EVE Online has this, if you're running Level 1 and 2 missions with a Destroyer. The enemy frigates you'll be shooting as part of these missions will go down pretty damn quick.
Of course, the Goombas of Super Mario Bros. They used to be allies of the Toads, their neighbors in the Mushroom Kingdom; however, they defected to Bowser's side, and have been The Chew Toys of gaming ever since.
It was recently revealed that they were actually created at the end of the first game's development, because the other main recurring enemy, the Koopa Troopas, required a two-step process to defeat, and the developers wanted to give players something simpler to defeat. (Ironically, in some of the newergames, Koopa Troopasare even weaker than Goombas!) Even Satoru Iwata, the current Nintendo president, was shocked at the fact that one of the most iconic Mario enemies was created last.
In Super Mario World, Rex took the Goomba spot (though each Rex took two hits to defeat), sharing it with unshelled Koopa Troopas. The Goombas did not show up early in the game, and when they did, they looked completely different and didn't go down with one Goomba Stomp. The Japanese version of World gave these Goombas a slightly different name (Kuribon) than the standard ones (Kuribo), so perhaps those Goombas are a different species of Goombas. Some fans call them "Round Goombas".
Don't forget the first monsters in Wario Land, the Gooms, which are completely unable to even hurt you.
Shellcreepers from Mario Bros. were The Goombas before there were Goombas.
Mega Man Zero gives us the Pantheons (with the most basic model, the Hunter, equipped with an Arm Cannon) in the first three games while the fourth game has them replaced with the Variants (similar to the Pantheons, but the most basic one having shots that burn on contact). The ZX series has both of them replaced with the Galleons, which - while an appearance that mixes both the Pantheon and the Variant - is functionally more identical to the Pantheons.
Zombies are solidly this, and so are skeletons for most of the series, but in the very first game skeletons are more of a medium-threat enemy, first showing up in the third stage and requiring significantly more skill to kill or get around than most of what you've faced so far. They're common enough to be Goombas in the fifth stage, though.
Gnawties, Neeks, Sneeks and Awks in the Donkey Kong Country games. The Kritters/Klomps/Kobbles/Tiki Goons aren't much stronger (though Diddy's peanuts in the Co-Op Multiplayer can stun the Tiki Goons, while they just kill the Awks outright); they're the Koopa Troopas of the series.
Also, the first kremlings you fight in Donkey Kong 64, which are before the first level, as well as the beavers.
In the first Spyro the Dragon game, the first homeworld is filled with Gnorc enemies that do nothing but run away from you, find a corner to hide in, and then tremble in terror when you approach them.
The Frogweed in The Legend of Spyro: A New Beginning and The Eternal Night. They take three hits to kill and you literally have to sit there and stare at them for them to have a chance to hurt you.
Yorps in Commander Keen Episode 1, which can't damage you themselves. The only way they can kill you is to push you into something dangerous. A similarly harmless enemy in Episode 2, the Scrubs, can actually be helpful as they can be ridden upon to access areas you otherwise couldn't. (they can climb up walls)
The Ghulibas in Eversion resemble Goombas at first; the file that contains their graphics is even called 'goomba'. In later stages the resemblance diminishes as they move faster and in X-8 after the 1.7.3 update, they regenerate after a short time.
Claw has, quite amusingly, Officers for those. (Soldiers are not very powerful either, but they have a ranged attack and can even qualify as Goddamned Bats) They can't block, take only one normal hit to die(one and a crouch in second level) and have a reaction time before they attack you (they really need to yell that "En Garde!" at you) which gives a player enough time to clock their face with a satisfying uppercut with impunity.
The Goombas of Wizardry VII: Crusaders of the Dark Savant consist mainly of slimes, birds, bugs, and plant-like creatures called phoots. Subverted in that later variants of these enemies range from annoying (spectral ravens) to incredibly dangerous even to advanced parties (shadow crusts, fire crows, bear weevils, mantraphoots).
Both Icewind Dale games tend to pit you against goblins as the first enemies that you have to fight. Of course, if your party is only level one at that moment, they are actually a fair match.
Baldur's Gate on the other hand, faced you off against diseased gibberlings (easy) and Wolves (much tougher).
The rat is the first enemy if you are starting in a dungeon. In Morrowind, it depends on were you go first.
A giant rat is also the first enemy in Daggerfall.
Very Very Empties are the weakest enemies in Eternal Sonata... as long as they don't duck into any shadows. As such, your encounters with them en route to Tenuto are in combat fields without shadows. Indeed, the first encounter is a very basic combat tutorial.
Both Fable I and Fable II use beetles. Both times they are also used in the "tutorial" (Guild Woods and the warehouse/Tomb)
Bandits in Fire Emblem. They're unusual in that they have plenty of HP and are able to inflict quite a bit of damage with each blow, but the axes they use are heavy and inaccurate, and most of your starting army can wield light and accurate swords. Later games gave swords the advantage in the weapon triangle, favoring the player even more.
The Maya type enemies in Persona 3. Most have several elemental weaknesses, low hit points and stats, useless skills and generally die in one or two hits.
Navy Jr. in Dubloon. First time you meet them while raiding Navi's ship, they are a little tougher than usual but pose no bigger challenge. By the time you meet them later in Navy HQ, they are so weak critical hits done to them with physical attacks will probably approach 1000.
Every act of Diablo 2 had one set of these buggers: The Fallen in act 1, the Mummies in act 2, the Pygmies in act 3, Oblivion Knights in act 4 (not particularly weak, but they still fit the pattern, in the context of act 4), and the Minions (the short, hunchback pig-men with spikes on their backs) in act 5.
Dark Souls has the Hollow Warriors in the Undead Burg. Easy to fight with their predictable movesets and large openings, they are nonetheless dangerous in groups.
In all Disgaea games except the first one, your very first battle is against a group of Prinnies. And even in the first game, Prinnies are the only generic units included in your initial party.
How Goomba-esque are they? Throw them (something you can do at will) and they blow up. And it only costs one Global Currency to bring them back from the dead.
Several weak demons take this role in most Shin Megami Tensei games. Traditionally, the weakest enemies are the Slime and the Pixy.
Each of the games in the Mario & Luigi series puts its own unique spin on the Goomba.
The first game, Superstar Saga, takes place in the Mushroom Kingdom's neighboring country, the Beanbean Kingdom, where everything is bean-themed instead of mushroom-themed. Their Goomba equivalent is the Beanie, a creature who looks like a bean with a face and two feet. Actual Goombas also appear in the game as training bosses. It should be noted that the actual weakest enemies in the game are Fighter Flies, who live on the border between the two kingdoms.
The second game, Partners in Time, takes place during an Alien Invasion. The weakest enemies in the game are alien Goombas called Shrooblets. Actual Goombas also appear later on, once again being tougher than normal.
The fourth game, Dream Team, features Grombas as the weakest enemy in the overworld, while Drombas are the weakest enemy in the Dream World. Actual Goombas appear as (somewhat late) midgame enemies where they usually work together with Fly Guys or each other to try to overwhelm Mario and Luigi, either through Zerg Rush (with other Goombas) or through Death from Above (with the help of the Fly Guys). They are even used as cavalry, being carried into battle by the Fly Guys to increase their numbers. Both Goombas and Fly Guys also have stronger versions of themselves that appear as mid-to-lategame enemies. Finally, Goombas remain one of the only enemies that are faced in both the real world, and the dream world (the latter as assisting enemies in a boss battle with the Elite Trio, one of which is a Goomba), and Dreamy Goombas can be summoned by the Final Boss, Dreamy Bowser.
Goombas actually got some respect in Paper Mario: The Thousand-Year Door where a few smart and competant ones (including two that were Mario's allies) appeared. In fact, while some Goombas in the game are still Mooks, some of them show some brains, wearing spiked helmets (apparently having learned from Mario stomping on them all the time).
Child Of Light has the giant grasshoppers. These have very low health, deal very weak damage, and have no special abilities. Once Aurora levels up once or so, she'll be taking them out in one hit.
Shoot Em Up
The enemy choppers in Twin Cobra and Twin Cobra II. They also have a red variant that has more health and is more dangerous.
Hominov Prop Planes in Heavy Weapon. These things take one hit to explode, but unlike another Mook that also dies in one hit, they have no weaponry at all.
Fairies in Touhou are incredibly weak and pose hardly any danger unless when doing Zerg Rush attacks. This being Touhou, it doesn't stay this way for long.
Which leads to a Running Gag: Ensemble Darkhorse ice fairy Cirno likes to proclaim, "I'm the strongest!" She actually is the strongest fairy. That, however, is like being the fastest snail - you're still a thousand miles behind everyone else.
Bakebake, sock-like ghosts who constantly trail their tongues fill this role for the PC-98 games, and half the time they don't even have an attack.
In Atomic Robo-Kid, the first type of enemy to appear is Bowles, blobby things that slowly drift across the screen, don't cause Collision Damage and are easy to kill with the weakest weapon. In the Mini-Boss battles, they drift continuously across the middle of the screen to block shots.
Whirlms from Viva Pinata are not enemies, but stupidly easy to tame.
Runners in Desert Moon. A similar enemy Bursters, are faster have more health, and explode on death. In fact, the final waves of the last three levels contain every enemy type except Runners.
Winston "The Rookie Killer" Payne fills this role in the Ace Attorney series, getting soundly trounced in each game's first case. He gets more pathetic with every game. His hair also gets sillier with each passing game.
The White Mouse from Mousehunt, being one of the weakest mice and also one of the first mice that you can catch. It also serves as the Mascot Mook, and has an Underground Monkey variant of it (the stronger Mutated White mouse).
Sauruses (or is that Sauri?) in Quest for Glory I fit the bill, as even a Thief or Magic User at the start of the game has a reasonable chance of taking one down. Lampshaded in the game itself by the Adventurer's Guildmaster, when he tells you anyone can kill a Saurus if asked about them. Goblins are also quite easy to defeat.
Quest For Glory I also has an "Experience" system, and after a certain cutoff point the game begins to spawn much stronger monsters, and it's entirely possible to advance so quickly you may never see the weaker enemies.
Desert Brigands in Quest for Glory II are by far that game's easiest and most commonly-encountered enemy.
Quest for Glory IV brings two: The badder (bats of a not goddammed variety) and vorpal bunny. Badders are a scripted first encounter, and there's a good chance of running into a vorpal bunny on your way to town after the opening. Badders only appear at night or indoors, but the bunny is probably the most common enemy during daylight hours.
StarCraft the Zergling their weak on their own, but in swarms they are a menace.
Homestuck has Imps and although at first they are shown to be a legitimate threat to low level players, they tend to get torn through pretty fast. That doesn't mean they can't get stronger...
Many Dungeons & Dragons DMs use goblins or kobolds as the PCs' very first enemies. That said, if the DM uses their abilities—sneaking and trapmaking, respectively—to their fullest (which few do), they can be very challenging indeed.
On the topic of kobolds, Crossfire has the 'unusual kobold' filling the role of the "superpowered Metal SlimeUnderground Monkey" subversion, with some ten thousand hit points and complete immunity to physical damage. They don't actually show up anywhere in the default mapset, however.
Just to underscore it, all three of those factions use their Goombas as emergency rations and/or tank fuel.
Anime and Manga
Zaku and its clones in Mobile SuitGundam multi-verse. In fact, they are named after the Japanese equivalent term "zako" (usually translated as "small-fry"). Ramba Rai's infamous "No Zaku" is showing that the story's has moved pass the basic level for Amuro.