Sgt. Barnes vs. Sgt. Elias (Platoon) – same side, Jerry Maguire vs. Bob Sugar (Jerry Maguire) – same agency, Martin Hansen vs. John Nash (A Beautiful Mind) – same class – all together, yet so far apart. Whether fighting against the Viet Cong, wrangling over elite sports prospects, or outgunning each other for a choice placement, each protagonist must face off against his nemisis: mano a mano.
The hero's nemesis is his or her worst enemy, usually someone or something that is the polar opposite of oneself, yet still shares a set of similar qualities or traits. In Sir Arthur Conan Doyle's The Adventures of Sherlock Holmes series, for example, Professor James Moriarty is the nemesis to Sherlock Holmes: both well-schooled intellectuals, gifted with critical, analytical minds, yet while Holmes uses logic for the good, Moriarty is a mastermind of evil.
Moriarty is Holmes' primary antagonist; however, a nemesis need not be limited to the primary villain alone. In fact, a nemesis is quite often used as a supporting rival character. He or she can even be considered a friendly troublemaker, someone who meticulously waits for a chance to mess things up for the hero, not because she wants to thwart the protagonist's ultimate goal, but quite simply because the nemesis hates the hero. Think Newman vs. Jerry (Seinfeld).
The irony of course is that if the hero is destroyed, the nemesis will have no one to hate; therefore, when push comes to shove, the nemesis will often join forces with the hero and fight together to conquer the primary antagonist. When this dynamic occurs, "The enemy of my enemy is my friend." (Arabian Proverb).