Gory takedowns can be satisfying, and say a lot about the characters we play.
Games are very good at satisfying fantasy violence and elaborate, gory executions are commonplace. These animations are partly there to shock and illicit that wincing "oof" when you watch your character dismember some unfortunate guard, but they are also there to make your moments of victory in a combat encounter stand out from the rest of the melee. A satisfying, decisive takedown is a release valve that gives you a moment to regroup before the fight resumes.
They are also useful for establishing character. Fight choreography can be used to say a lot about your avatar's mindset. Jackie in the Darkness 2 is sadistic, and worryingly inventive with his demon arms, as though he has spent far too much time thinking about how to use them. In Shadow of Mordor, Talion is quick and decisive with his deathblows—the technique of a warrior used to fighting many enemies at once. Agent 47 is efficient and wastes no energy on flair, as you would expect from a seasoned professional.
We started discussing memorable melee attack and takedowns that work particularly well in the context of the game world in which they feature. Violence in games rarely analysed. It is discussed in terms of 'is this bad?' rather than 'how did they make this so satisfying?' Here is a collection of games that do it well. Warning: if you don't want to see lots of pretend polygonal NPCs get beaten up, shot, and stabbed (a lot) look away now.
Dark Messiah of Might & Magic delighted in the Source engine's ragdoll physics systems, and integrated them into its combat system with the excellent kick move. Booted foes fly through the air, taking out destructible terrain and getting stuck on spikes. Might & Magic's levels find many contrived ways for you to finish fights using this signature melee attack. Those spiky panels are everywhere.
Hitman is, of course, all about killing people in horrible ways, but there is something especially mean about the hammer attack in Hitman: Blood Money. Perhaps its the directness of the attack, combined with the use of such an ordinary everyday tool, that makes it so effective. Agent 47's animations all express a psychopathic nonchalance that well befits a contract killer.
Jensen's melee attacks demand so much energy that you might not see all of his takedown animations. They are remarkably elaborate and inventive. The developers had to create a fighting style for a guy who can shoot blades out of his wrists and elbows—a futuristic martial art. Some of the moves are comedic—the double headbutt is great—but the one where Jensen unhinges his hand and spins it to throw his enemy is so crazy and alien it sells Jensen as the terrifying futuristic commando he's supposed to be.
There is an outstanding level in Arkham Knight when Batman teams up with Robin to infiltrate a hideout. You can switch between characters, order each other about and join forces to beat up the Joker's goons. The Arkham games use Batman's brutish takedown animations to sell his powerful, direct method of fighting. The co-op takedowns take this to another level, contrasting Batman and Robin's styles in moments of superheroic teamwork. The Arkham games use slow motion to create snapshot moments that look like living comic book panels.
Every weapon type in Brotherhood has its own set of complex multi-foe takedowns that Ezio executes with dazzling, horrifying efficiency. The Assassin's Creed games always feature spectacular choreography but Brotherhood's takedowns are particularly elegant, often using aggressor's momentum and weapons against other enemies. Ezio is skilled, but he is only human, so Brotherhood's combat relies on technical martial prowess rather than absurd feats of strength (see Deus Ex: Human Revolution and the Batman Arkham games for that). There is obviously a lot of martial arts expertise on the development team, and the resulting takedowns really sell the idea of the assassin as a master of all weapons.
Violence is a form of catharsis in a revenge fantasy, and Dishonored 2's gory knife finishers are a grisly vector for Corvo and Emily's fury. Dishonored's art style produces guards with of an almost caricature appearance. Their features are exaggerated and they are unusually expressive. This, combined with the close first-person perspective, makes these executions uncomfortably intimate. They are pretty graphic, but the violence of Dishonored 2's executions add extra weight to the lethal/nonlethal decisions at the heart of the game.
Being and Orc in Shadow of Mordor has to be one of the worst jobs going in PC gaming. Talion is absolutely merciless. Shadow of Mordor's take on the Arkham knight combat system benefits from the addition of a very sharp sword and a dismemberment system. The flash of a blade, backed up by some excellent slashy sword noises, sells the execution. There are no Legolas-style flourishes here, only the straightforward aggression of a trained soldier looking for the fastest killing blow possible.