One-on-one fights can be fun, but what if you don't want a whole episode or scene dedicated to just one person showing off? That's how you get Goku doing the same Kamehameha for three episodes. Sometimes what you want isn't a tight focus on a couple of characters, it's a melee that brings in a full cast. Another thing that great anime fight scenes need are high stakes. While a fight to the death isn't the only way to make viewers care about the outcome, it's a pretty effective method.
Sometimes the most exciting thing is a straight up battle royale in which a huge group of characters get in on the fight. This can occur in a single arc or even an episode, as it does in Naruto and Kino's Journey, but it can also take up the entirety of the plot, as it does in Future Diary and Deadman Wonderland.
Which are the best battle royale anime? That's up to you.
Each version of the Fate series differs in its content and themes, but one thing they most have in common is the epic showdown that is the Holy Grail War. Whoever gets their hands on the grail can have any wish granted, but getting there will require doing battle with a plethora of incredible weapons, including one sword so powerful that they literally created the earth. Plenty of blood will be shed in pursuit of the grail, but who will emerge victorious?
Future Diary is an anime entirely dedicated to the concept of battle royales. Twelve people are given magical diaries that allow them to predict the future in various ways, and are told to fight to the death using the information they receive. Whoever is left gets an incredible reward - to inherit the position of the God of Time and Space. Everyone else dies horrifically - so whether the participants actually want to be gods or not, they have no choice but to participate if they want to survive.
Not every part of Hunter x Hunter focuses on a battle royale, but the fourth stage of the Hunter Exam serves as a thrilling exception. Gon and the other participants are let loose on an island, where their job is to take possession of each other's badges. This wouldn't necessarily be a death match, except for the presence of Hisoka, a kill-happy clown who uses the competition as an opportunity to lay waste to as many people as he possibly can. What keeps Gon alive is less his battle skills than his strategic abilities, but it's still pretty gratifying to watch him come out on top with the help of his trusty fishing pole.
Fullmetal Alchemist: Brotherhood isn't a battle royale anime per se, but it's final battle certainly qualifies. The main antagonist, Father, is attempting to harvest the souls of thousands of Amestrians in order to fortify his body so that it can act as a "container" for God - essentially, giving himself godlike powers. Edward Elric and his fellow state alchemists, plus Hoenheim, Scar, and a ton of other people who aren't into Father becoming an all powerful god team up to beat him. It's one of the most epic free-for-alls in anime history, and its amazing that there were only a few casualties.