Last week we talked about the Hero archetype but now I want to talk about something different. As always, we're going to take a look at using the Nemesis in writing, but we're also going to look at how the Nemesis can be used in game design.
The oft-overlooked archetype is the Nemesis. They are as potent as a hero for telling a good story, and they can take many forms. Although it is possible for heroes to face a "nemesis" that is not a person, a writer making that decision is making a decision to have the hero face the world rather than another person.
After all, if the word nemesis just means "the inescapable agent of someone's or something's downfall" (thanks, Google), there is nothing to say that agent has to be a person.
But many of the most interesting stories have a nemesis—a capital N Nemesis—be a person.
Why?
Well, there are actually several reasons.
First, we relate to people. Having a character struggle against the force of nature and Being is a good enough story in and of itself, but this struggle will always have a certain static element to it. Even if the protagonist's conception of nature or society change, it is not necessarily possible for these large systems to change (though societies can change, and do change, this is something that doesn't usually happen until after the hero has conquered them, or after they have conquered the hero: Okonkwo in Things Fall Apart is a great example of this as a tragic hero).
Second, a Nemesis will explore a psychological space the hero doesn't. Tragic heroes, like Faust, spend a certain amount of time in the shared mindset of their Nemesis, but with more traditional or epic heroes the Nemesis is going to take one of two forms: the antithesis or the flawed apotheosis.

Nemesis as Antithesis

The Nemesis as antithesis is something that we see quite often in more traditionally conservative storytelling. If you have a Christ, then you have an Antichrist. That's a simple equation for a nemesis.
There are a few reasons why you might want a Nemesis to be an antithesis of your hero.
The first, of course, is if you are posing a diametrically opposed worldview or morality against your own. To use the example of the Christ, who brings forgiveness and transcendence, versus the Antichrist, who offers dominance and rapacious power, there's a very clear reason why your Nemesis is going to be the exact opposite of your hero.
After all, if you're trying to tell a moral story, you don't want someone failing.
This is also true for other philosophical or political works; Orwell and Rand both use villains who adhere to the philosophy that runs contrary to their own (both, ironically, feature totalitarian villains, though the authors' views of each others' political philosophies would be dismal).
This comes with a certain number of pitfalls. For one thing, it's very easy to create a strawman when trying to build a Nemesis; just look at the number of Christian movies that end with a cheap comeuppance against a pesky atheist (looking at you, God's Not Dead 2, which is perhaps something I don't necessarily want to confess to watching).
Another issue is that such a Nemesis often comes across as blatantly malicious. While this is occasionally a solid premise (Silence of the Lambs springs to mind), it is also something that can be absolutely rubbish if done poorly. Such stories fail to deliver on the deeper meaning that their authors often want to achieve, reverting to a classic dualistic approach to good and evil rather than a significant investigation of any moral or philosophical lessons.
Antithesis nemeses can also run into an issue with heroes where they do not simply have any logical reason to interact. Usually, when you see such characters pop up it's in comedies, where a plucky underdog unseats some confident and successful jerk. In more serious stories this is dangerous, and in roleplaying games, where the players are likely to pursue goals in exploration of their roles, it may result in a storyteller preparing for things that are simply unlikely to happen.
If you look at many of the greatest nemeses in roleplaying (Strahd pops to mind, with the caveat being that some adventurers will have him more as a flawed apotheosis since they are equally amoral), they cannot simply be subscribing to an alternate lifestyle than the heroes. They must have commonalities in some axes of their lifestyle, but have a philosophical difference and entirely different motives.
It's also important to note that the antithesis nemesis will not run into direct conflict with the hero unless they somehow have opposing interests. Batman and the Joker in The Dark Knight are a perfect example of this, despite the various philosophical musings, since Batman is a clear representative of Order and the Joker is a clear representative of Chaos. It is their methods that bring them closer to each other, but their philosophies that make them adversaries.

Examples

I want to give a few examples of this process:

Ready Player One

Hero: Cyberpunk protagonist pursuing safety and good times (Innocent and Fool archetypes)
Nemesis: Corporate elites wanting power and control (Ruler archetypes)

Sherlock Holmes

Hero: Sherlock Holmes (really?), world's greatest detective and criminologist
Nemesis: Moriarty, world's greatest criminal/murderer/psychopath/jerk

Moriarty, by Sidney Paget

The Lord of the Rings

Heroes: Frodo, Gandalf, Legolas, free people seeking to end a machine of power
Nemesis: Sauron, Saruman, thralls of evil forces and magical chaos

Eclipse Phase

Heroes: Anarchists seeking immortality and transhumanism
Nemesis: Virus that removes independent agency (and provokes DOOM-esque hyperviolence)

DOOM

Hero: One nameless space marine silent protagonist wish-fulfillment vector (player avatar)
Nemesis: Incarnate evil, sometimes corrupt corporations
It's worth taking a moment and noting the role of games as a tool of player agency and that they allow a player to make a particular sort of statement. There's a particular power as a storyteller in being able to tell such a story that the player agrees entirely with your premise and makes the same decisions you would (in a linear story).
At the same time, the most annoying storytelling in games assumes that you are going to agree with the writer's assertions. When you combine this with a player avatar as the protagonist, you're going to provoke a violently bad reaction. This is where EA's flawed Syndicate reboot ran into trouble with me during the single-player (I enjoyed the mindless FPS elements, but the silent protagonist made obvious mistakes at every corner and did things that I would never have done given a choice) and where the Mindjammer tabletop game got me so worked up I quit reviewing games.
Seriously. As a storyteller you want to avoid creating a premise that your audience is going to disagree with and then shouting it at them instead of trying to build a rapport with your argumentation. Orwell did a fantastic job of this as a video game that really let you make decisions with some moral and philosophical weight to them, and I highly recommend it to people looking for a good case study in using games to tell stories. It doesn't necessarily fit as a true antithesis nemesis situation, because the player's own political views will inform the relationship, but it's a great use of a society as nemesis. Five stars out of five.

Nemesis as Flawed Apotheosis

The other sort of Nemesis is the one that has a nearly identical philosophy and worldview to the story's protagonist, but winds up with one or two pivotal values changed. This is a powerful tool for encouraging self-reflection and having a sort of revulsion pop-up between the hero and Nemesis (and maybe even in your audience, if they're of the right sort).
The character who stands out to me as a flawed apotheosis is Kurtz, from Heart of Darkness. He and the protagonist start in very similar ways, but they quickly find that the road to Hell is paved with good intentions.
Where the hero sees the destruction of Kurtz' wake, Kurtz only sees the setbacks as a confirmation for his own toxic ideology confirming the natives of the Congo, convinced that the destruction he is causing to them is proof of his notion of their racial inferiority and servile nature. Because he is able to gain power over them, and they eventually come to fearfully worship him, he is able to find validation of something that the more reasonable protagonist realizes is entirely evil.
The reason that the flawed apotheosis is so important is that it embraces the concept of evil within the self; that there is some element of danger in all of us. This is an oft-denied statement, even as the people who deny its truth in their own lives turn to another group and point out their rougher edges.
The flawed apotheosis is an effective Nemesis because, at some point, they were the hero, or something very like the hero. Many nemeses pretend to be this, because it is a great psychological weapon, so you need to be careful here (for instance, the Emperor trying to taunt Luke Skywalker into falling to the dark side of the force, or Satan tempting Christ in the desert by pointing out that they are both incredibly powerful and could rule the world).
The great thing about the flawed apotheosis is that they often can be the central point of the story, with their actions requiring the hero to come at things from a different approach to prove their merit. It allows the hero to be shown in comparison to a great, but tragic, character, who falls to their inner Shadow (more on that later).

Examples

The Dark Knight

Hero: Batman
Nemesis: Harvey Dent
Harvey Dent is basically the public and legitimate equivalent to Batman, a renegade who pursues good ends. However, he cannot withstand the trials inflicted upon him by the Joker and falls into a villainous Two-Face persona.

Les Miserables

Hero: Jean Valjean
Nemesis: Javert
Javert and Jean Valjean both pursue justice as one of their highest goals, with Valjean trying to live a life that views justice as a product of intent and outcome, while Javert considers the law to be the highest form of justice.

Using Nemeses in Storytelling

The simple rule of thumb for a Nemesis in storytelling is that they should be a source of stress for the hero that drives growth and introspection.
So how does a Nemesis work in a game context?
This is fairly obvious as a goal for most people making games to tell stories, as every game has a problem or a "bad guy" that needs to be taken care of.
However, there are a few things that should be considered with regards to how you approach this in your own works.
In an interpretation of Paranoia where Friend Computer is malevolent or entirely dysfunctional, it often becomes an antithesis nemesis, since Friend Computer is an omnipotent machine and the player characters reflect the futility of humanity in the bureaucracy. Anti-heroes are great for exploring the antithesis nemesis, especially when they are fighting Kafka-esque designs and bureaucracy.
These nemeses need hardly be worked into the game mechanics, though something like Betrayal at the House on the Hill's timers or resources devoted to the nemesis could be useful. They can work as narrative devices, or in the case of something like the elder gods in Call of Cthulhu simply ignore the standing rules for most characters and do their own thing.
For the flawed apotheosis approach, however, your nemeses need to have a strong mechanical presence. They are the players' character(s), only stronger, faster, and twisted. The best way to think of a nemesis in this form is as a tragic hero who got away with it.
In Jungian psychology, there is a notion of a Shadow that resides within a person's being. This Shadow reflects the dark desires and temptations they are susceptible to, the things that they shouldn't do that they wind up doing anyway if they are weak or unprepared.
Your Nemesis has to have at least played with fire and succumbed to elements of their Shadow if you want the protagonists to be heroes (of course, if you have evil or amoral protagonists this is not the case). In some cases, they are controlled by it, or even revere it as their virtue, thinking that their new way of doing things is good while their old way was naive.
Each of these methods is a distinct approach worthy of its own consideration: is your Nemesis a good person who went too far, a person who wants to be good but has not made that choice, or a person who is so messed up that they can't figure out the relationship between good or evil?

Two-Minute Breakdown

The most important element of a nemesis, however, in both storytelling as a writer and storytelling as a game designer is that they should not be cheap. They are not just an evil +1 version of the hero, they are an incarnation of sin. They do not need to be evil, even. Javert and Friend Computer consider themselves—and rightly by some standards—to be incarnations of goodness.