Great anime fights don't have to involve legendary weapons, intricate elemental powers, or anything complicated. Sure, those kinds of fights can be amazing, but sometimes all you need is the brutal, raw strength that comes from hand-to-hand combat. The best hand-to-hand fights in anime are just as exciting as the more complex battles, especially when they have great animation to back them up.
One particularly memorable fight is from Naruto - Kakashi and Obito have plenty of powers outside of their punches, but the intimacy of hand-to-hand combat helps underscore their fraught relationship. There's also Ohma versus Raian from Kengan Ashura, a fight that proves that CGI can be glorious in the right hands.