In most of the combat oriented manga and anime. The plots tend to feature a hero and a villain inexorably drawn together (to the credit of the genre, usually by their own choices rather than fate) who will eventually be locked into a duel. Besides making for highly enthralling action oriented entertainment, there is a purpose to this other than gratuitous violence.
This is a thematic function that is intrinsically tied to the idea of Bushido. One of the precepts of Bushido is that the practitioner is already dead. This means that in battle he has nothing left to lose and thus is not fighting at all: what he is fighting for fights through him. the warrior is only an instrument of his beliefs.
This is why you can't just watch the final episode of an anime and get the jist of what it was all about. Since the warriors are metaphors of their own ideals, the duel is a philosophical debate (albeit, a very vivid one). If you were to watch You only see two guys fighting. Had you seen the story from the beginning, you'd know what each character involved represents and why the hero wins as well as understanding the consequences he suffers afterwards.
Probably the easiest example to work with is Rurouni Kenshin. Himura Kenshin, the protagonist, is an ex-assassin who has become a pacifist when he learns what true loss of human life means. That process is symbolized by a cross-shaped scar on his cheek. It is not a Christian symbol, but the vertical stroke is the wound he inflicted on society which never healed until he received the second, horizontal one which marked his change to pacifism. Consequently, he renounces his political affiliation and uses only a sakabatou (a sword with the sharp side facing the wielder so that it can't cut anyone). He thus represents a humanistic pacifism that can only see fighting as a tragedy and a last resort.
Shishio was Kenshin's successor in the role of revolutionary assassin and is his first major foil. He espouses a theory of social Darwinism whereby the strong can come to rule over the weak.
So, basically, they fight, Kenshin wins, and humanistic pacifism beats Social Darwinism any day of the week. And twice on Sundays.
In recapitulation, the tradition of the duel in anime and manga is both an entertaining one and an agile, if simplistic, method of philosophical discussion.