An Arch-Enemy, archfoe, archnemesis or simply nemesis is some character's designated and most important enemy.
The Arch-Enemy can be the Big Bad, The Dragon, The Rival, an Evil Counterpart, or even a Harmless Villain. The essential element is that, with them, It's Personal. Most typically, the Arch-Enemy is a foil of some sort, usually a mirror foil. For example, the Arch-Enemy of the physically strong could be very smart. If there is a Greater-Scope Villain, his Arch-Enemy commonly is the Greater-Scope Paragon.
The Arch-Enemy will stand out from the Super Hero's Rogues Gallery — there will be one opponent where the relationship to the hero and the motivations for battling them are more potent. These feelings may be one-sided, felt more by the villain than the hero, or occasionally vice-versa.
A hero's Arch-Enemy is not necessarily the biggest threat to them. Lex Luthor is considered Superman's Arch-Enemy; Brainiac is smarter, and both Brainiac and Darkseid are vastly more powerful and dangerous, but for Lex — and, to a lesser extent, for Superman — it's personal between them. Additionally, although Superman has battled many foes of great power and strength, Luthor is still seen as his Arch-Enemy because to a general audience, he's viewed as the most iconic and recognizable of all of Superman's rogues.
Sometimes, the hero could have made the same choices as the Arch-Enemy: the Arch-Enemy is showing us what he could have become, as in the case of Batman and the Joker.
A hero may possess more than one Arch-Enemy if more than one villain from his Rogues Gallery stand out, or if a former Arch-Enemy dies and new one comes in to the picture. As an example, consider Spider-Man: the Green Goblin, Doctor Octopus, and Venom have all established themselves as recurring and iconic foes of Spider-Man, each of whom has been considered the wallcrawler's Arch-Enemy at different points in time.
Lastly, remember that this generally refers to the enemy the hero considers to be his Arch-Enemy, and ideally, it should be personal on both sides (though there are plenty of good "But for Me, It Was Tuesday"-type Arch Foes out there). Especially in the case of a Rogues Gallery, the hero is usually considered an Arch-Enemy to all of his villains, but he doesn't treat all of them as such. Electro, Rhino, Scorpion, and others all consider Spider-Man their most hated foe, but compared to the Goblin, Venom, or Doc Ock, Spidey regards these guys more like superpowered nuisances. Also, remember that being the Big Bad does not automatically make a villain the hero's Arch-Enemy. For instance, it could be that the hero's enmity with The Dragon is far more personal than the one they have with their master; see It's Personal with the Dragon. Sometimes, a villain becomes the Arch-Enemy of the hero when the villain does something that makes the hero realize that they are Beyond Redemption.
Beware of letting an Arch-Enemy fall victim to Villain Decay.
See also Breakout Villain, for those instances when a run-of-the-mill villain ascends to Arch-Enemy status.
Not to be confused with various works known as Nemesis. Also not to be confused with the Swedish melodic death metal band. Technically, the word "nemesis" originally referred to an agent of divine justice or retribution for egotistical thinking; thus Batman could be described as Joker's nemesis, but not vice versa.
