Mooks but No Bosses

Nowadays, the vast majority of video games, even when not pure action games, include fighting enemies on the way. There may be a lot of weak ones or a few tough ones, they may be humans or monsters, you may kill them half-heartedly or with great enjoyment but they will be on your path to prevent you from Saving the World, rescuing the Damsel in Distress, finding your lost memories or eating your pizza. And at some points, you will have to fight big enemies, much more fearsome and dangerous than the others (or not…) with an appropriate tension buildup.

But some games go around this. Even though you fight your way through numerous Mooks and death traps, no climactic battle against a boss ever comes. There can be several ways to explain and/or compensate the absence of bosses:

The fighting, even if present is actually secondary to the action and the developers want to focus the intensity on other aspects, like the general atmosphere or the HSQ of the scenario.
The climactic battle(s) will be against an army of mooks instead of a single boss, placing the player against seemingly impossible odds to create tension.
Sometimes, you expect enemies to be bosses, but they are fought and finished every bit like normal Mooks in the end. The difference with a mere Anticlimax Boss being that they aren't just easy, they are identical to Mooks so you can't call it a Boss Fight.

Polar opposite of a Boss Game where all the fights are Boss Fights. Not incompatible with Cutscene Boss.

Note this trope is about the absence of bosses in a genre where their presence is the norm. Endless Games and Construction and Management Games are generally bossless for obvious reasons, as well as Strategy Games where the notion of "Boss Battle" is pretty much meaningless (potential aversions may be added as examples though). And of course, no need to list the games where there are no enemies in the first place.

The extreme end of Hard Levels Easy Bosses.

Examples of Mooks but No Bosses include:

Action Adventure

In Soul Reaver 2, a good part of the game is slaughtering the soldiers and demons who want you dead, but curiously, there is no Boss. The Sarafan counterparts or Raziel's "brothers" at the end seem like they will be bosses but they turn out being like normal mooks, just tougher, and the Soul Reaver prevents you from dying anyway. The real Oh Crap moment comes after this battle.
In the Batman Begins game, you fight Victor Zsasz, the Scarecrow and Henri Ducard, but they fight in exactly the same way as the Mooks, right down to the way they're taken down.
The videogame adaptation of The Godfather. The "bosses" are the dons of the other families but they're easy to kill, the real challenge is fighting all their mooks.
In Uncharted 3, the closest thing to boss fights in this game are basic fistfights against a guy who has a bit more HP than usual.
In Tomb Raider III, every single artifact you come across is guarded by a boss character who uses the powers of the artifact to kill you. However, the Element 115 artifact in the Nevada level is only guarded by regular mooks and has no one trying to use the said artifact to kill you. Since the levels by region can be played in any order you want, some players may feel a bit cheated that the artifact isn't guarded by an epic boss.

First Person Shooters

The Call of Duty series never really had any bosses, with practically all enemies fighting the same and taking the same number of bullets to kill. Modern Warfare 2 upped the ante with the addition of Juggernauts, but in general all the major, plot relevant foes are either killed in a cutscene, quick time event, or as easily as any other mook.
The Halo series is known for this, with Halo 2 being the only real exception. The boss fights in Halo 2 were highly criticized, so apparently Bungie decided boss fights just weren't their thing.

Platformers

The 2D PlayStation game Heart of Darkness is like this. The final battle is against a huge number of mooks but you never actually fight the Evil Overlord, he's just destroyed in the following cutscene.
The first two Oddworld games involve killing a lot of guards in usually gruesome ways, but since Abe has no weapon nor actual fighting skills there is nothing in the games that looks like a Boss (well there are "bosses" but not in the video game sense).
The Platform Hell Rick Dangerous.
Every level in the Commander Keen games is devoid of bosses, with the exception of the final level in the third (the Grand Intellect), fifth (the Shikadi Master) and spin-off episodes (Boobus Tuber).
The second episode (game) of Cosmos Cosmic Adventure doesn't have any bosses at all, and the first and third only have a Final Boss (the same in both cases).
Eversion has no bosses, but it makes up for that with its more famous attributes.
Dustforce. The boss-looking Evil Counterparts from the intro and trailer are actually multiplayer characters.

Roguelikes

In Azure Dreams, all combat takes place within a tower teeming with monsters, but with no unique encounters. The powerful sorceror Beldo waits on the top floor, but it's impossible to actually lose to him

Role Playing Games

Deus Ex: You do engage several elite enemy operatives, but they are not much stronger than a regular mook, if better armed and augmented, and die almost just as easily.
- The same is true of the sequel, Deus Ex: Invisible War. Probably even more so than the original, as all the elite operatives were just regular enemies with somewhat more health. They didn't even have any special abilities even though plot-wise they were supposed to.
Mass Effect 3: There's only one boss in the game, and he's closer to a beefed-up Phantom than anything. That said, fighting 3 Banshees and 3 Brutes all at the same time is no picnic.
The Ultima series in general is known for not having bosses at all, with many of the games being more about actual role-playing than pure combat. Some of the games do have a final confrontation against a unique enemy, but they're usually not noticeably tougher than regular enemies.

Third Person Shooters

In Max Payne, there were many fights against "boss" mobsters who could withstand boss levels of punishment before being defeated. Max Payne 2 does away with these fights almost completely. There's only one enemy who's at all tougher than a regular Mook, Kaufman, and even he goes down in less than a dozen shots. The final boss fight is mostly a Puzzle Boss, although you do shoot him up after solving the puzzle. Max Payne 3 is mostly like Max Payne 2 in this regard, although there is one boss fight against an armored Giant Mook about 4/5ths of the way through the game.

Wide Open Sandbox

In Red Dead Redemption, the closest thing there is to a Boss Fight is Edgar Ross in the epilogue but it's played like a normal duel (except you don't have the option of sparing his life). As for John's old companions, two are summary executions and the last throws himself from a cliff.
Spore: the closest thing is has are Grox and even then they act more like Elite Mooks.
The nearest you'll ever get to a boss in L.A. Noire is an important enemy with a slighly better gun than usual, unusual car chase (such as the one against a tram), or the occasional scripted Good Old Fisticuffs fight or "shoot the villain before he shoots the hostage" minigame. The emphasis being on detective work.