Incredibly Durable Enemies

"The enemies are too strong, which is fine, but it's annoying when every single thing you try to blow up takes so much gunfire. Even when you're in the present time, there's no bad guys that die with one shot. And I understand when you're shooting the Terminators; they're made of metal, but these are human beings."

—The Angry Video Game Nerd on The Terminator for the Sega CD

In some games, it takes an absurd amount of firepower to take down a basic enemy, whether due to monsters simply having massive amounts of Hit Points, weapons being PVP-Balanced, or a combination of both. Maybe its only when the game's difficulty is cranked up to "Make It Hurt!". Rats take multiple pistol rounds, Humanoid Aliens take repeated shotgun blasts to the face, and even with a rocket launcher there are still some guys that are going to go through a Death of a Thousand Cuts. This concept can apply to magic and melee weapons as well.

These opponents aren't Goddamned Bats, much less Demonic Spiders: the monsters aren't Made of Iron (or at least they aren't supposed to be) and if they were Boss-level opponents there might be some excuse. But no, these are just the average, every day, run-of-the-mill Mooks. And it takes an entire arsenal to put them down.

If this is combined with your character being a One-Hit-Point Wonder, just put down the controller and walk away...

Related to Kung Fu-Proof Mook.

Examples of Incredibly Durable Enemies include:

Diablo II: Unless you have nice equipment, don't expect enemies to drop from a single cast of Meteor, Armageddon, or Fist of the Heavens.
Doom: The baron of hell, despite being only a little bigger than a human, takes five or six direct hits from the rocket launcher or double-barreled shotgun. Then there's the Cyberdemon, who takes several shots from the BFG to down. Although that at least is understandable, since he is The Dragon.
Unreal: Even the weakest skaarj takes a full, 50-round, clip from the combat assault rifle before he goes down. The Titan, Warlord, and Queen can all take dozens of rockets.
A lot of MMORPGs fall into this, but none are half so bad as Dungeons & Dragons Online. At the early levels, you're trained to think that bad guys will die after 3-5 hits. At the highest levels, it's a whole different mess. Without the best and rarest equipment, it can take 15 to 30 hits just to take a minion down.
- More like 15 to 30 hits WITH the best and rarest equipment. And that's for the easier minions. The harder ones have over 9,000 HP. Literally.
- Dungeons and Dragons itself does this, but only to the players and not to nearly the same extent.
Max Payne: Some mooks take several point-blank shots to drop.
Gears of War: The basic Locust will tear you apart if you're not in cover. (And even IF you're in cover. You might run out of damn ammo.) It takes almost a full magazine of assault rifle fire to kill just one of these guys. On Insane, you had to shoot enemies in the head in order to avoid running out of ammunition entirely.
- This became much less the case with time. In Gear of War 1, fighting without using the cover system, even if you were just walking behind the pillar to avoid fire, was suicidal even on the lowest difficulty. By the time Gears of War 3 came around, on normal mode, you had a good chance of survival even if you made liberal usage of bayonet charges. Oh, and the enemies seemingly became more fragile over time too.
The skags in Borderlands are this in the early game.
In Fallout 3 a normal person can expect to survive two or three head shots from a submachine gun without flinching.
When you crank up the difficulty in the Devil May Cry games, this trope is in full effect. In most of the games in the series it's done to an acceptable degree and the worst of it can be avoided with skillful playing, but 3 makes fighting most of the enemies in their Super Mode mandatory and strategically attempting to avoid what triggers them to transform (number of enemies killed, ie. weakening all the enemies next to no health before killing off any of them so you can finish them off quicker when they do transform) only helps to fix the situation to a very minor degree, causing the game to crossover from legimately challenging to this trope in its worst form.
When Halo is set on legendary, elites and brutes can take an unholy amount of damage before their shields burst, and almost as much again to kill them unless you go for the head with a suitable weapon. It is possible to run through dual wielded SMG clips even when they are fully on target against a red elite, not even an Elite Mook, and still have them survive a melee attack. And don't get me started on the white elites. (Equivalent of the elite special forces in the first game, who wore black armour.)
The Elder Scrolls Oblivion on the hardest difficulty has crabs and rats that can easily finish your character off. When the rats can kill you off with little difficulty, you know you're playing a hard game. Min-Maxing is the key to success here. Normally though, rats go down in a few hits. The game seems to go up a few magnitudes in difficulty on the hardest setting.
This is one of the many reasons why the Shoot'Em Up game Steel Saviour is Nintendo Hard.
There are enemies in the penultimate level of Evil Dead: Fistful of Boomstick that are freaking bullet sponges, meaning you'll be heading into the last level with virtually no ammunition - unless you thought to try the flamethrower on them, which kills them in a second or two (and considering the videogame flamethrower's typical effectiveness, you probably didn't).
Many Tower Defense games, especially when it gets to the last few waves. The enemies become from cannon fodder to these.
It varies based on where in the series it takes place, but in the course of the Mechwarrior series you'll end up fighting a lot of enemies, sometimes of a vehicular nature (especially in 3 and 4), but most often you'll end up facing enemy 'Mechs. Even the smallest ones seem to be uncannily tough, with even spindly lightweights like the Owens or Osiris taking quite a while to bring down by the time the 4th installment comes around.
Bug!! has this in later levels. Most of the Mooks in the first two levels take around 1-2 hits to be killed (two of them take five, one's a rarely-seen Demonic Spider and the other is a Helpful Mook). Then you get to the next four levels, where almost all the regular Mooks take at least three hits to kill.
The PlayStation 2 FPS Black had enemies that took so many rounds to kill that learning to headshot was mandatory on the easiest setting. Perhaps this is the reason all your guns hold ridiculous amounts of bullets.
The Juggernauts from the Call of Duty franchise embody this trope. In a game where a few shots is enough to take down the typical enemy these guys require relentless ammo to be poured into them before keeling over. According to the Call of Duty wiki in Mordern Warefare 2 killing them requires "almost 80 rounds of assault rifle fire, at least five Intervention sniper rifle torso shots, around 14 shotgun blasts, or five-six direct hits from a M203 40mm grenade launcher to kill. "
The opponents in the Cruel Melee version of the Super Smash Bros.. series' Multi Mook Melee. Usually the only way to defeat them is with gimp KO's as actually getting them to a high enough damage to hit them out of bounds is extremely difficult.