9 Movie Heroes & Villains That Didn't Know Each Other Existed
2. Korben Dallas & Zorg - The Fifth Element

Perhaps the all-time best and most amusing example of this is in cult classic sci-fi actioner The Fifth Element, where heroic cabbie Korben Dallas (Bruce Willis) and evil industrialist Jean-Baptiste Emanuel Zorg (Gary Oldman) are blissfully unaware of one another.
Even though they're direct rivals both pursuing the four mystical stones which can save Earth, neither meets the other nor do they ever know who each other are.
Korben has no idea of Zorg and his crusade, while Zorg hasn't a clue that Korben is on his own mission to battle the Mangalores and retrieve the stones, and this carries all the way through to the very end of the movie.
Writer-director Luc Besson seemingly wants the audience to appreciate the strangeness of this, given that he even shows the pair barely missing one another while riding successive elevators mid-way through the story.
Much as you can argue that The Great Evil itself is the real villain of the Fifth Element - given that it's a giant fireball with plans to wipe out Earth and all - Zorg is the villain with the greatest presence throughout the film, so this definitely counts.